depends
By "game" you mean deer (or bigger) of course. The state land I hunt does not allow MV off established roadways. I have a a game "cart" and where location allows, I go back to the Bronco and roll the cart in to the animal, then roll it out. If to thick or steep for the cart, I drag. My treestand harness has a drag ring attachment at the low rear. I clip into the deer and the drag ring and point my nose in the easiest direction and puff. When I can get the cart there, I do. As a teen, Bamaboy was my mule and liked to show me how well he could drag, sadly, the guy has a big boy job and a wife now, I've lost my mule.
I have an ATV too, an older 2WD straddle version, and on a lot of private property/leases, I can get pretty close with it, if not just right there. A manual "come-along" type winch up front lets me hoist the deer on the rear rack w/o busting a gut muscle. I use the ATV at my skinning shed to hoist the animal to the rafters.