Why does Rashi bother defining ויגר?

Parashat Balak begins (pesukim and Rashi):

Balak the son of Zippor saw all that Israel had done to the Amorites.		ב. וַיַּרְא בָּלָק בֶּן צִפּוֹר אֵת כָּל אֲשֶׁר עָשָׂה יִשְׂרָאֵל לָאֱמֹרִי:
Balak… saw all that Israel had done to the Amorites: He said, “These two kings whom we relied on could not resist them; we certainly cannot.” Consequently, “Moab became terrified.” - [Mid. Tanchuma Balak 2, Num. Rabbah 20:2]		וירא בלק בן צפור את כל אשר עשה ישראל לאמורי: אמר אלו שני מלכים שהיינו בטוחים עליהם לא עמדו בפניהם, אנו על אחת כמה וכמה. לפיכך ויגר מואב:
3. Moab became terrified of the people, for they were numerous, and Moab became disgusted because of the children of Israel.		ג. וַיָּגָר מוֹאָב מִפְּנֵי הָעָם מְאֹד כִּי רַב הוּא וַיָּקָץ מוֹאָב מִפְּנֵי בְּנֵי יִשְׂרָאֵל:
[Moab] became terrified: [Heb. וַיָּגָר is] a term denoting dread, as in,“Fear (גּוּרוּ) for yourselves” (Job 19:29). - [Machbereth Menachem p. 59, third def.]		ויגר: לשון מורא, כמו (איוב יט, כט) גורו לכם

The following analysis, from R' Ovadia miBartenura, is reprinted in the sefer Prachei Rashi:

That is, he starts with a slightly different citation of Rashi, which stuffs together the first Rashi (אמר אלו שני מלכים) with the beginning of the second (לשון מורא). R' Ovadia miBartenura writes:

"It is difficult, that which Rashi needs to explain from what Balak was afraid, for the pasuk explains the basis for his fear! It is further difficult why he needs to explain that ויגר is a language of fear, for this is obvious! 

And there is to say, and resolve these matters, in the following manner: Since the pasuk did not say 'And Balak the king of Moav saw", we derive that Balak was not primary in this matter. And further, since it is written after that 'And Moav feared", and it is not written 'And Balak feared', the seeing was ascribed to Balak and the fear to Moav.  

Therefore it seems appropriate to explain that Balak himself did not take the choice in this matter, but rather Moav; they were the ones who employed the stratagems. But the seeing was ascribed to Balak to tell you that even Balak ben Tzipor, who was a mighty warrior known for his might, as is written (in Shofetim 11) "are you really better than Balak ben Tzipor?", even he directed his heart to see all that Israel had done to the Emorites, but he did not fear as Moav feared, for he was not yet king over them, as Rashi explains soon (pasuk 4, d"h בעת ההוא). And since Moav saw that even Balak saw and put in his heart to contemplate the matter, they were quite scared and frightened. And this is what Rashi explains, 'therefore, ויגר מואב." That is to say, because of the seeing of Balak, they were afraid. 

And Rashi needed to explain ויגר as a language of fear because I could have explained it as a language of gathering, such as אוגר בקיץ, and like לא תגורו מפני איש, which they darshen as don't enter in your words, and I would have explained that Balak commanded to gather in Moav and to enter them into the fortified cities because of fear of Israel. 

Therefore he explained ויגר as a language of fear, because it is not possible to explain it as gathering, because the word מאד (the adverb 'greatly'), which follows it, does not apply to it: וַיָּגָר מוֹאָב מִפְּנֵי הָעָם מְאֹד. Meanwhile, as a language of fear, the word מאד can apply, that is to say, they feared greatly."

End quote.

This is an interesting and creative explanation, but I believe that it reads way too much into Rashi. If Rashi meant something so elaborate and non-obvious, I would have expected him to say more.

I don't know the answers to these questions, but I can venture a guess or two, based on Rashi's sources. Like a true golem, I will consider the ויגר as fear first.

That pasuk and Rashi again:

Moab became terrified of the people, for they were numerous, and Moab became disgusted because of the children of Israel.		ג. וַיָּגָר מוֹאָב מִפְּנֵי הָעָם מְאֹד כִּי רַב הוּא וַיָּקָץ מוֹאָב מִפְּנֵי בְּנֵי יִשְׂרָאֵל:
[Moab] became terrified: [Heb. וַיָּגָר is] a term denoting dread, as in,“Fear (גּוּרוּ) for yourselves” (Job 19:29). - [Machbereth Menachem p. 59, third def.]		ויגר: לשון מורא, כמו (איוב יט, כט) גורו לכם

So Rashi is citing Menachem ben Saruk. That might be reason enough for this comment, since Rashi often cited Machberet Menachem, and this is citation / channeling of sources rather than necessarily being entirely bothered by something such that Rashi is prompted to comment. We have access to Machberet Menachem, here. The entry starts on page 58 and continues on to page 59, for the root גר, and he gives 11 different definitions of the root. And the third definition reads:

The fourth definition is asifa, gathering, just as Bartenura mentioned. There are other definitions, such as dwelling. Or this one also might be plausible, given the context of Moav: וַיֹּאמֶר ה' אֵלַי 'אֶל תָּצַר אֶת מוֹאָב וְאַל תִּתְגָּר בָּם מִלְחָמָה.

I would guess that because this is a relatively uncommon word, and because there are 11 possible definitions, and because it is the subject of an entry in Menachem ben Saruk's dictionary, Rashi believed that it was appropriate to clarify, and to offer another example, taking from the first words of the dictionary entry. This doesn't mean (contra Bartenura) that Rashi really considered alternatives, such as 'gathering', remotely plausible, if not for the adverb מאד.

Another reason Rashi perhaps saw fit to define ויגר is that the midrash Tanchuma (one of Rashi's primary sources) actually interprets this in several different ways, the last of which is indeed fear. Thus (siman 2):

ויגר מואב 

מהו ויגר? 
כשהיו ישראל נראין לעמונים, נראים עטופים לשלום. 
וכשנראים למואבים, נראים מזויינים למלחמה, שכך כתיב: וקרבת מול בני עמון, אל תצורם (דב' ב יט). 
כתיב: למלחמה, שכך כתיב: וקרבת מול בני עמון, אל תצורם (דב' ב יט) 
כתיב: כל מין צרה אל תצר להם. 

ואל תתגר בם (שם) כל מין גירוי. 
ולמואבים אמר: אל תצר את מואב ואל תתגר בם מלחמה (שם שם ט). 
מלחמה אין אתה עושה, ומה שאתה יכול לחטוף מן החוץ, חטוף. 
ולפיכך נראים מזויינים, והם נאגרין לעריהם, שאין ויגר אלא לשון אסיפה, שנאמר: אוגר בקיץ בן משכיל (משלי י ה).

While referencing וְאַל תִּתְגָּר בָּם מִלְחָמָה, in the end the midrash interprets this as gathering. Despite the word מאד.

And next, meaning to dwell in non-permanent fashion:

דבר אחר: 
ויגר לשון גר, שהיו רואין לעצמן כגרים בעולם. 
ואמרו: ירדו למצרים לגור והאחזו אותה, והיו משכירין להם בתים, שנאמר: ושאלה אשה משכנתה ומגרת ביתה(שמות ג כב). 

And finally, fear:

דבר אחר: 
ויגרלשון יראה, שהיו מתיראין, שראו כל הארץ ביד ישראל, שבא סיחון ונטל ארץ מואב, שנאמר: והוא נלחם במלך מואב הראשון וגו' ( במ' כא כו). 
ועוג נטל את כל ארץ בני עמון, שנאמר: כי רק עוג מלך הבשן נשאר מיתר הרפאים וגו' (דבר' ג יא). 
באו ישראל נטלוה משניהם, גזל שאין בו עולה. 
והיו אלו רואים את ארצם ביד ישראל, והיו אומרים: לא אמר הקדוש ברוך הוא, כי לא אתן לך מארצו ירושה (שם ב ט), והרי ארצנו לפניהם, לכך היו מתיראין. 

If so, Rashi is selecting from amongst the various midrashic interpretations and choosing the one which is peshat.

Turning now to what Balak saw, I don't think that we can sustain R' Ovadia miBartenura's assertion that Balak didn't fear but merely contemplated. After all, Rashi is channeling Tanchuma (and all these also appear in Bemidbar Rabba):

משל למה הדבר דומה? 
למלך שהושיב שומרים לשמרו מן הגייס, והוא בטוח עליהם שהיו גיבורים. עבר הגייס והרגם, והיה מרתת על עצמו. 
ואף כך בלק ראה מה נעשה בסיחון ובעוג שהיה מעלה להם שכר לשמרו והיה מתיירא מעצמו. ועוד שראה נסים שעשה להם הקדוש ברוך הוא בנחלי ארנון. 

The midrash explicitly says that Balak was afraid, והיה מתיירא מעצמו. It is true that both Rashi and midrash Tanchuma mention that Balak was appointed after the killing of Sichon:

at that time: He was not entitled to the monarchy. He was one of the Midianite nobles [according to some: of the nobles of Sihon (Josh. 13:21)], and when Sihon died, they appointed him over them on a temporary basis. — [Mid. Tanchuma Balak 4, Num. Rabbah 20:4]

בעת ההוא: לא היה ראוי למלכות. מנסיכי מדין היה, וכיון שמת סיחון מנוהו עליהם לצורך שעה:

However, he could still be afraid, given his new role as king. And see the previous perek, Bemidbar 21, where the Israelites attack and kill Og after attacking and killing Sichon.

Furthermore, while it might be obvious what Balak was afraid of from the very words of the pasuk, אֵת כָּל אֲשֶׁר עָשָׂה יִשְׂרָאֵל לָאֱמֹרִי, once we realize that Rashi is channeling his sources and selecting what to say, we know that Rashi actually did have a choice and has made a selection here.

Namely, Balak could either have been afraid because of the death of Sichon and Og -- which is personal, and also accords with the simple peshat of the pasuk. Or, he could have been afraid because of the miracles at Nachal Arnon. To cite that Midrash Tanchuma again, which is Rashi's source:

ואף כך בלק ראה מה נעשה בסיחון ובעוג שהיה מעלה להם שכר לשמרו והיה מתיירא מעצמו. ועוד שראה נסים שעשה להם הקדוש ברוך הוא בנחלי ארנון.

The Midrash points to the deaths of Sichon and Og as well as  the miracles at Nachlei Arnon.

And those miracles, while not explicit in the Biblical text, were in fact brought into scope by Rashi on the previous perek:

Concerning this it is told in the account of the Wars of the Lord, "What He gave at the [Sea of] Reeds and the streams of Arnon.		יד. עַל כֵּן יֵאָמַר בְּסֵפֶר מִלְחֲמֹת יְהֹוָה אֶת וָהֵב בְּסוּפָה וְאֶת הַנְּחָלִים אַרְנוֹן:
Concerning this it is told: Concerning this encampment, and the miracles that happened there, “it is told in the account of the wars of the Lord”: when they relate the miracles that happened to our forefathers, they will relate: “What He gave….”		על כן: על חניה זו ונסים שנעשו בה יאמר בספר מלחמות ה', כשמספרים נסים שנעשו לאבותינו יספרו את והב וגו':
What He gave: Heb. אֶת וָהֵב, like אֶת יָהֵב [which is the Aramaic root meaning to give]. Just as from [the root] יעד we say ועד so from יהב ‘to give’ [we get] והב, and the “vav” is [part of] the root. That is to say, what He gave (יהב) them and wrought many miracles at the Red Sea. — [Onkelos]		את והב: כמו את יהב, כמו שיאמר מן יעד ועד, כן יאמר מן יהב והב. והוי"ו יסוד הוא, כלומר את אשר יהב להם הרבה נסים בים סוף:
and the streams of Arnon: Just as we recount the miracles of the Red Sea, so should we recount the miracles that happened at the streams of Arnon, for here too, many great miracles were performed. What were those miracles?…- [Midrash Tanchuma Chukkath 20, Num. Rabbah 19:25]		ואת הנחלים ארנון: כשם שמספרים בנסי ים סוף, כך יש לספר בנסי נחלי ארנון, שאף כאן נעשו נסים גדולים. ומה הם הנסים:
15. And the spilling of the streams that turned to settle at Ar and leaned toward the border of Moab.		טו. וְאֶשֶׁד הַנְּחָלִים אֲשֶׁר נָטָה לְשֶׁבֶת עָר וְנִשְׁעַן לִגְבוּל מוֹאָב:
The spilling of the streams: The Aramaic translation of שֶׁפֶךְ,“spilling,” is אֶשֶׁד -the spilling of the streams, for [there] the blood of the Amorites who were hidden there was spilled. The mountains were high and the gorge deep and narrow, and the mountains were so close to each other, that a man standing on the mountain on one side [of the gorge] could speak to his fellow standing on the mountain on the other side. A road passed along [the floor of] the gorge. The Amorites said, “When the Israelites enter the land by passing through the gorge, we will come out of the caves in the mountains above them and kill them with arrows and stones shot from catapults.” There were clefts in the rock on the Moabite side [of the canyon], and directly opposite those clefts, on the mountain on the Amorite side, there were protrusions, [appearing] like horns and breasts. When the Israelites prepared to pass through, the mountain of the Land of Israel trembled, like a maidservant going out to greet her mistress, and moved toward the mountain of Moab. Then those breastlike protrusions entered the clefts, killing them [the Amorites]. This is the meaning of, “that turned to settle at Ar.” The mountain swung from its place and moved toward the side of the Moabite border, and attached itself to it. Thus, “[it] leaned on the border of Moab.” - [Midrash Tanchuma Chukkath 20, Num. Rabbah 19:25]		ואשד הנחלים: תרגום של שפך אשד. שפך הנחלים שנשפך שם דם אמוריים שהיו נחבאים שם, לפי שהיו ההרים גבוהים והנחל עמוק וקצר וההרים סמוכים זה לזה, אדם עומד על ההר מזה ומדבר עם חבירו בהר מזה, והדרך עובר תוך הנחל. אמרו אמוריים כשיכנסו ישראל לתוך הנחל לעבור, נצא מן המערות בהרים שלמעלה מהם ונהרגם בחצים ואבני בליסטראות. והיו אותן הנקעים בהר של צד מואב ובהר של צד אמוריים היו כנגד אותן נקעים כמין קרנות ושדים בולטין לחוץ, כיון שבאו ישראל לעבור נזעדזע ההר של ארץ ישראל, כשפחה היוצאת להקביל פני גבירתה, ונתקרב לצד הר של מואב ונכנסו אותן השדים לתוך אותן נקעים והרגום. וזהו אשר נטה לשבת ער, שההר נטה ממקומו ונתקרב לצד גבול מואב ונדבק בו, וזהו ונשען לגבול מואב:

I'll just add that it is plausible that Rashi's, and the midrash's, explanation regarding Sichon and Og is not peshat, but is rather derash. That is, Emori could either mean the Emorite people or specific Emorite persons. La-Emori might mean to Sichon or to Og, rather than the Emorite people. Sichon and Og as protectors and warriors, rather than Sichon and Og and stand-ins for the battle with these Emorite people. And this midrashic explanation is non-obvious.

Finally, there is the juxtaposition Rashi makes of לפיכך ויגר מואב. I think that Rashi is grappling with an irregularity of change in topic, that first Balak sees and then Moav fears (much like R' Ovadia miBartenura mentioned). But Rashi isn't making any nuanced diyuk of it, based on Balak not being called a melech. Rather, there is a shift, in that we know that Balak saw, but we don't see Balak's reaction. Meanwhile, Moav's reaction in the next pasuk might be read as a self-contained item -- they feared because of how numerous the Israelites were. That is what was bothering Rashi. Rashi chooses to merge the two in meaning, that the fear was first set into motion by the acknowledgement and contemplation by the Moabites and by the Moabite leadership of the deaths of Sichon and Og, such that they had reason to fear. So pasuk 2 leads naturally towards the reaction in pasuk 3.