Breeding any game clocks to game hens would still produce game chicks. I cross different game breeds all the time and the results are much more exciting than pure breeds. The trick is to breed traits that you want to keep like; color (feather or leg), weight/height, speed/strength, agressive/docile etc.
"Pure breeding" is problematic in my opinion, because to keep something pure you need to breed relatives and that sometimes results in genetic abnormalities. Pure breeding is usually predicatable but their may be unlying health issues, similar to pure bred dogs versus mutts. American Games are just hybrids between Oriental Game, Red Jungle Fowl and Old English Game.
You can breed a game chicken to a regular chicken and the result would be either game or not; 50/50 chance... (game refers to the aggressive nature). You can breed that hybrid back to another game and the result would most likely be game, but with some of the other traits of the non-game bird. For example you can get bearded (muffed) game chickens from crossing Ameraucanas with Game, which my friend did.