The game is a version of Tic-Tac-Toe, except this version is played on a 2-by-2 grid.
Role in episode
Patrick tries to make his own game, which leads him to creating a fast and easier version of Tic-Tac-Toe called "Tic-Tac." He starts playing it with Squidward, who keeps winning because he goes first every time. After many games, Patrick gives up on the game.