Is "contre" essential for this to make sense? Could you say "il combat des animaux"?
you are right. "il se bat contre des animaux" and "il combat des animaux".
verb "combattre" already contains the notion of "with" (or against in English) with "com" (latin = with)
Although it certainly clarifies from "il combat avec des animaux", where the animals are presumably aiding in the fight, not the subjects of the fight.
you are right, the nuance is exactly there.