Why is Stay Puft even in the cartoon?

That was never explained in the cartoon. One possibility is that after the ecto marshmallow was cleaned up, it was stored in the Ecto Containment Unit and recongealed in the same form it last had--Mr. Stay Puft. But since Gozer's intelligence had been shifted back to it's own dimension, Stay Puft was mindless and then developed a simple, childlike personality.