I like the idea of simply stopping the game. Noisy disruptions = Forfeit game, I think is a good lesson in consequences and choice. I am wary of having kids associate studying with punishment, though, so I never do writing as punishment (I know you didn't mention that). I sometimes do a couple minutes of silent waiting (and hope no one gets the giggles).
Do you worry that your kids will starting thinking of study time as the punishingly dull part of the lesson, and the game time as the best part? Just curious how you deal with that. I don't know if it's just me being wishy-washy or what.