Sure, here's a simple game that meets your requirements. It's a game where you have to tap the square to change its color between yellow, red, green, pink, blue, and purple. You score points each time you tap on the square.
To play the game, simply save the above code into a file with an `.html` extension (e.g., `color_game.html`), and open it in a web browser on your smartphone. Tap the square to change its color and score points!