This cat is doing something that we rarely see and he/she is doing it voluntarily because it pleases him. The video is entitled “Gizmo the crazy upside down cat”. I’d say he is not crazy at all but typically very flexible, agile and athletic as all domestic cats are. In truth, the behaviour is not strange either. It is just something he can do easily and he therefore does it. In short, it is what it is.
He wants to groom and mess around with his tail and gets easy access to it when upside down! Of course, he could get easy access to his tail sitting down which would have been easier but the fact is that it is not difficult for him to take up this extreme position (by our standards). It looks extreme to us but is comfortable to him.
He is probably a bit bored and is finding ways to alleviate it.