Note: In general the sign "game" is done with a double movement and the fronts of the fists make contact two times.
But I've seen highly skilled signers like Dennis Platt (wonderful guy, world traveler, heavily involved with Deaf sports events, and former president of the Utah Association for the Deaf) do the sign "game" using a single strong movement without the hands touching.
So, here is my advice: When you are referring board games or simple little games between a two players then go ahead and do this sign with a double movement with the knuckles of the hands butting up against each other similar to the way rams butt their heads together. (That's just a memory aid. Do the sign lightly so as to not hurt yourself.) If you are referring to a sports match you can do the movement one time and you can make contact but you don't "have to" bring them all the way together. Either way is fine.
