I don't know, but I wonder if your parent commenter is making a philosophical point about the potentially illusory nature of owning a group of semi-wild animals. Like, if the only way you have of asserting your ownership is to use them as a food source, then do you really "own" them? Or do they exist outside and apart from human ideas of property?

Or like owning a mountain or a centuries-old tree. Does that even mean anything?

Owning is, like, a human construct man. If you can slaughter a herd of animals without facing any human imposed consequences, it's probably fair within the bounds of language and meaning to say that you own them.

Pierson v. Post 3 Cai. R. 175 (1805) is instructive. Your post is a great starting point for exploration of basic property law. TLDR ownership consists of a varied bundle of many different kinds of rights which can arise in many different and possibly conflicting ways.