You can get model aircraft jet engines with enough power for this.[1] Various human-carrying craft have been built that way, such as the Zapata Flyboard.[2] But the engines have a lifespan measured in hours and not enough reliability for carrying humans. That's why all the demo videos of these things are over water, or tethered.
People have been trying to build small, cheap jet engines for decades. "Small" has been done. Cheap, no. Below bizjet size, the price doesn't go down much. Which is why general aviation is still running mostly on pistons. The 1960s Williams jetpack (not the Bell rocket belt) used an engine intended for cruise missiles.
If they've cracked the small jet engine problem, there's a big market for those, without trying to package them as jetpacks or motorcycles. Otherwise, it's just another demo rig.
The video is a bit suspicious. It's very quiet. You can hear the boats over it. It doesn't blow stuff around. It doesn't move his clothing. It doesn't ripple the water even at low altitude. Other videos of small jet engines are very noisy and have lots of jet blast.
[1] http://www.jetcat.de/jetcat/Kataloge/JetCat%20ENGINES.pdf