If you look closely at the video, you’ll see a technician pull a cable off the machine and there are some flashing greet indicators suggesting some kind of electronics. The 3D gyro packages found in consumer drones are dirt cheap, so you have to wonder if something like that has been adapted here.
The two jets we know of that hover–the AV-8 Harrier and the F-35–use vectored thrust to do that. I could imagine the engines on some kind of small limited motion gimbal to do that, but I have no idea if that’s what’s going on. Could it even be some kind of nozzle vector, such as the F-22 has? It can actually hover, too, although pointed straight up. Dunno.
Someone asked why he did this over water and I think I know why. Any kind of failure at low altitude could lead to loss of control with insufficient altitude to deploy a parachute. The wing has a fast acting jettison system and its own parachute, so if he does jettison, it’s an easily survivable fall to the water. That wouldn’t be true over land.
There must be some kind of coffin corner between about 25 feet and maybe 300 feet, above which a reserve or BASE-type parachute might be deployable. Above that and climbing, he’s got more options. I hope more detail about it will become available because I think it’s a real breakthrough in human flight, even if it lacks commercial legs.