The answer to the question is yes.
But it's also species dependent.
Animals with short lifespans are typically a food for other animals with longer lifespans. So anxiety over interrupting evolutionary processes via hunting is probably misplaced. Most small prey animals have high birth rates, high annual mortality.
And it's been shown that hunter participation is tied to perceived likelihood of success. So, hunters are mostly compensatory on small game.
All that said, which is the central tendency for a shotgun website, Man absolutely changes the evolutionary processes within target species of longer lived game animals. Specifically the mega fauna and cervids.
Animals with a social structure (like Elephants) depend on a complete breadth of age class to teach age specific behaviors. That's one of the reasons elephant herds are so strictly managed.
I eat wild fish and game nearly everyday. And always have it in my freezers.
