This is a Pachinko game (Japanese Pinball), a mix of slot machine and pinball. The player has to controll the speed with which many small steel balls are thrown into the pachinko machine.
Most of the balls just fall down the machine and disappear, but a few find their way into special holes. This activates a kind of slot machine. Like with slot machines, you win if the same three pictures appear.
This is a one button game, because only one button is needed to play it.