I can think of one game, but unfortunately, you can only carry 100 pounds of food back to your wagon. -Regardless or how many animals you shoot. It runs on an Apple lle though.
The publishers of Big Game hunter has a whole line of them. They were a huge fad back in the 90’s. I don’t think any modern publishers have gone with it, but really, it’s a perfect genre for PC or the Wii.
There’s a game called Afrika on the ps3 that’s about taking pictures of African wildlife. I think that fits what you’re looking for as long as shooting pictures instead of bullets will work with whatever you had in mind.