To avoid confusion I am referring to the sport of hunting games usually animals
The best hunting themed video game in my opinion. actually used to be free online to get on PC it's called the "Carnivores" series. It is a dinosaur hunting games that is nothing like the Turok series is.
In Carnivores you actually hunt dinosaurs, and live game in a free roaming map worlds. You don't just shoot any dinosaur, instead you have to shoot the dinosaurs you chose to hunt to earn points. But you are allowed to kill whatever you want anyway, this game has no restrictions. But shooting the wrong dinosaur is a waste of time and ammo and that is not how you progress in this game.
You earn points by shooting the dinosaur or dinosaurs you chosen to kill. Or tranquilize at the beginning of each and every hunt. These points allow you to unlock more weapons, and dinosaur licences, as well as maps to hunt on. Also you can enable things like a dino radar to find dinosaurs instantly, and a stink spray to go undetected. Also you can choose to wear camouflage also, but using any of those will deduct the amount of point you earn in a hunt.
Last but not least you can die, and get eaten by a dinosaur including a T-rex, or Raptor or other kind of dangerous creature. And lets say you killed a dinosaur and after that you died, all the points you earned during that hunt will not count.