This is the classic "Tanks" game, except instead of a hillside with gravity, it is played on a rotating disc. The disc starts off spinning slowly, and increases in speed with each level.
The left-hand image shows the view from above, from a camera fixed in space. The right-hand image shows the view from above, from a camera fixed to the rotating disc. Due to the Coriolis effect, the bullets appear to follow curved paths when observed from within the rotating disc (the right-hand view).
You score 1 point for hitting an opponent and lose 1 point for hitting yourself. The walls on the disc block the bullets. Good luck.