Assuming there is no correlation between "game" in the pit and the dog's abilities to perform outside of the pit, unless you are planning to fight the dog, who cares about game? To me it's like bragging about how you dog comes from a line of great racers yet all you and your dog do is lay around the house. I guess I don't see the benefit of calling a dog game or game breed. The whole thing seems like an ego trip to me.
Like Woody said, if that's not a gamebred pup according to your standards then so be it. I still think M. Carver put gamebred pups on the ground, whether he tested his brood matrons or not and produced more game dogs than most of us have. Not to mention how successful he had become in the dog game. But I guess he had no common sense... "Jim" from down the street wouldn't even come close.
Having said all of that, I say I have "gamebred" dogs most of all to distinguish that I own the "old style" APBT and face it, most lay people out there have no idea what "Old Style" means, but they do know what Gamebred means.