Huh, looking just at the link at the top of the box, and forgetting the remainder of the links, this cannot work. I tried it with a flat cable. If you rotate it like that, it becomes twisted.
(update: I was wrong, not the wiki page)
It is indeed easy to twist the belt until you have the hang of it.
I think the animation is a bit deceptive because even with elastic bands you'd have to provide some way for the correct untwisting to occur. In the animation it happens 'automagically'.