The trigger and maybe the hammer could be broken if the sear is in a hammer notch and the gun drops on the hammer. Of course, I certainly hope that the gun is unloaded while playing games.
I used to play some of those games, but stopped when I dropped a gun; no harm done, but it seemed pointless. If I were going to take it up again, I would get one of those aluminum dummy guns that wouldn't be harmed if dropped.
Jim