Well, given that you're doing a class, I would hope that all the students would be at the same level? Perhaps you could do a game where you start with one move, and then go around the room, your next student has to do the move you did, and then add another move of their choosing. As you go around the room, each student adds a move, till it comes around to you again, and then maybe everyone has to do the whole thing in sequence?
You could encourage people to add flourishes, hair flips and things that make the "routine" theirs. You could also try to keep it solidly with the moves they've learned in class with you, or at a certain level (such as banning inversions if not everyone can do them safely, or sticking to grounded-only moves, so that there are no full spins, ect.)
You could also have a class where you work on few moves, such as three, and just see what people can come up with, how to transition into and out of the moves, how to go from one to the next, and see what they can do during the move to make it more dynamic, make it theirs, make a pose include movement, and such. Not exactly a game, but it's something I plan on working on more and more, and I would love to see classes doing that!