Fit Cats is a logic-puzzle game with a merge element similar to 2048 and the Watermelon (Suika) game. The player drops different sizes and types of cat heads into an open cardboard box to merge two matching heads at a time to create larger, new types. Their primary goal is to earn a lot of points and make all the heads fit into the box. The game also provides them with a secondary goal of catching mice that appear and disappear in various spots in a room with a highly stylized post-modern theme.
The player drops a cat head into the box using a white, dashed vertical line to direct their drop. They can check the upper-right corner of the screen to see the next head available to strategically drop the heads. Since the heads bounce and roll, they must carefully direct and time the shots to prevent small heads from blocking the merging of larger ones.
Unlike similar games, Fit Cats has no horizontal warning line that the player must never allow the heads to cross. Instead, the player must never allow the heads to stack so high that one rolls over the side flaps, falls into the room, and drops below the bottom of the screen.