R. Yehoshua ibn Shuaib writes (in his Derashot to Parashat Balak) that it was another book (no longer extant) available in chazal's time (see San 106b) and credited as Moshe's authorship. He says that what appears in parashat Balak was a more resumed portion of that book.
רמב"ן הקדמה לבראשית
בראשית. משה רבינו כתב הספר הזה עם התורה כולה מפיו של הקדוש ברוך הוא
זה אמת וברור הוא שכל התורה מתחלת ספר בראשית עד לעיני כל ישראל נאמרה מפיו של הקדוש ברוך הוא לאזניו של משה
Ramban's Introduction to Bereishis
Bereishis. Moses wrote this book [Bereishis] along with the the entire Torah from the mouth of ...
I don’t know for sure, since it isn't clarified further by the Midrash or other parallel Midrashim that I found. However, here are a couple of related points, which may qualify as an answer:
In Sefer Kasa Depischa, he suggests that this "Narga" was actually Moshe's staff, and proceeds to ask a question based on that. If so, he had his staff with him ...
I know you are asking about 100 fold damage, But The Gemora in Moed Katan 16b answers a question regarding why David could not cause 1000 fold damage mentioned in Devarim 32,30:
על שמונה מאות חלל בפעם אחת שהיה זורק חץ ומפיל שמונה מאות חלל בפעם אחת והיה מתאנח על מאתים דכתיב (דברים לב, ל) איכה ירדף אחד אלף
The expression: “Against eight hundred people, ...
The lands that are attached to the promised land by war (of any kind) becomes a real part of Eretz Israel even if outside of the originally promised borders, so they were in fact, in Eretz Israel, like somebody in Eilat today (the fact they have 2 days of yom tov is just because they are far from Jerusalem, but they are in fact inside Eretz Israel.
The pasuk can be taken as literature parse and shouldn't be taken literally, just like:
Lev 26, 37
וְהַנִּשְׁאָרִ֣ים בָּכֶ֔ם וְהֵבֵ֤אתִי מֹ֙רֶךְ֙ בִּלְבָבָ֔ם בְּאַרְצֹ֖ת
אֹיְבֵיהֶ֑ם וְרָדַ֣ף אֹתָ֗ם ק֚וֹל עָלֶ֣ה נִדָּ֔ף וְנָס֧וּ
מְנֻֽסַת־חֶ֛רֶב וְנָפְל֖וּ וְאֵ֥ין רֹדֵֽף׃
As for those of you who survive, I will cast a faintness into their hearts in ...
You should compare apples to apples, not to oranges.
Abraham wasn't in a war, while Moses was.
Actually, god wanted this raid to be an act of vengence, so maybe there is no place for mercy here.
Bameedbar 31 2
נקם נקמת בני ישראל מאת המדינים אחר תאסף אל עמי
Avenge the vengeance of Israel from the Midianites, Afterwards you will die.