Most fishing and hunting games do have animals often kept in zoos, though probably not in the context we want them to be in lol
Red Dead Redemption and especially its sequel has lots of animals that look and behave close to their real-life counterparts, including Gila Monsters, Roseate Spoonbills, American Black and Grizzly bears as well as many others.
Metal Gear Solid 3 : Snake eater lives up to its name as you can capture and eat snakes including Coral snakes and Reticulated pythons. It also allows you to hunt and eat birds, reptiles, inverts, fish, markhor and gharial? I confess I've never actually played the game
In Gibbon: Beyond the Trees, you play as a non-specified species of gibbon and brachiate your way throughout a non-specific Southeast Asian country. This one is on my wishlist.
In Webbed you play as a peacock spider (Maratus sp.), while I don't think this is an animal ever kept in zoos, in the game your mate is captured by a Satin Bowerbird.