Sure! Here's an example of a simple game that meets your specifications. The game involves tapping on smiley faces that appear randomly on the screen. You can play it on a smartphone.
To play the game, you can open this HTML file in a browser on your smartphone. It will display a black screen, and smiley faces will appear randomly every second. Tap on the smiley faces to increase your score. The score will be displayed at the top. You can stop the game by pressing the 'Escape' key on a keyboard.