I marinate or dry rub all cuts of game for a day before eating (except Elk), people don't know they're eating wild game unless I tell them.
As for ground game meats, I'm usually making chili, bolognese sauce, taco meat, etc. so again, so much spice that you wouldn't know the difference.
I've never really had an issue with anything tasting "too gamey" unless I meant to prepare it that way or the meat was freezerburned or something.
I just think it's 90% in the cooking method/preparation... 10% in the processing, IMO.