How will Hashem fight the Goyim?
Malbim: I explained in Yechezkel that He will send panic among the two combatants, and man will kill his brother. This will be via His Hashgachah. It is considered that He fights.
What is "k'Yom Hilachamo b'Yom Krav"?
Rashi citing Targum Yonasan: Like the day that He arranged war at Yam Suf. Radak ? Krav is war, like "Tovah Chochmah mi'Klei Krav" (Koheles 9:18). The verse did not explain which war; Yonason explained, the war at Yam Suf. Then Yisrael were in great distress, for the Egyptians were chasing after them. Moshe told them "Hashem Yilachem Lachem v'Atem Tacharishun" (Shemos 14:14). Also here, it says "v'Nilcham ba'Goyim ha'Hem"!
Malbim: Krav is always fighting an enemy nearby, with contact. Milchamah can be from afar, via arrows, [slingshot or catapult] rocks? Here it teaches that Hashem will not fight from afar via natural causes, rather, nearby, not via intermediaries, rather, with miraculous Divine power.