I know what you're thinking, but this inventor is not just talking about the usual method of swinging on a swing, which he himself notes has been "known for generations." It would be stupid to try to patent that. This patent covers only the method of pulling alternately on the ropes or chains in order to generate side-to-side motion.
Update: as several of you have since pointed out, this patent was later re-examined and invalidated after it came under fire for being ridiculous. So you could argue that the episode shows that the system actually does work (eventually).
Longer update to follow.