It is very difficult to believe, even as you're watching it.
Unfortunately, we don't know a whole lot of details about what exactly in the hell we're seeing here. This drift Prius was filmed at the Tokyo Auto Salon, and it has obviously had some pretty major work done. Including being converted to rear-wheel-drive. There does seem to be some electric whine, so it's quite possibly still a hybrid. We don't know exactly how that would work, this isn't exactly the sort of thing you see too often.
It's pretty entertaining, if just for the weirdness of the whole thing, but that's still a perfectly good reason to watch.