In Hopping Mappy players control the Micro Police mouse, Mappy as he bounces on a pogo stick to run circles around pink cats, called Meowkies, who patrol either vertically or horizontally. There is also Nyamco, a cat who patrols in a zigzag pattern, but he needs to take occasional breaks. There are eight treasures that a player must grab to complete a round, except on the bonus round where the player will just want to collect all the balloons that he can. The main intrigue here is getting past a blockade of Meowkies.
The player controls are simple - Mappy can bounce in any of the four directions, the only places he can land are the centres of the checkerboard squares (making for very few locations overall), and he will move at the same speed as the cats. If the player pushes the accelerator button and runs around, he will go twice as fast. When the cats have sped up (after a "Hurry Up" warning has appeared) they will match Mappy's accelerated speed.