From the Super Mario Wiki
In this microgame, the player controls a dog. This dog is chained to a peg, which is the center of what is going to be a circle. In the first difficulty, a small section of said circle isn't yet drawn, so the dog needs to walk on the blank spot, which magically draws it. Once the circle is complete, the peg and the dog's chain disappear and the circle now has the dog's face in it. Both the dog and the circle grin at the player. For the second difficulty, there are two parts of the circle that are blank. Once again, the dog needs to fill in the blanks. For the third difficulty, most of the circle will be missing, and for the third time, the dog will need to run over the blank spots.