How is a plane with only ailerons and jet (no props) controlled?
The ailerons in most flying wings can also move together up and down, then working as an elevator. This is called an &quot;elevon&quot;, combining both words as the device is combining both functions. Since flying wings mostly use reflex airfoils, loads on the rear part of the wing tend to be small and the force to keep elevons at their right deflection is small, too. In case of the SB-13, they are pre-loaded by a small, adjustable spring but otherwise free-floating.
In this case, however, it could be that they only work as ailerons.
When used for pitch control, elevons must move up and down together on both sides. This means they will be freely floating and must be held in position by some force. It would be easier to cross-link them so they only can move against each other, and then they only work as ailerons.
The airplane, called OpenSky M-02, is the brainchild of Tokyo University of the Art professor Kazuhiko Hachiya and has been built by Aircraft Olympos of Japan. OpenSky M-01 was a lighter, unpowered version.
As Louise Hose writes on Kitplanes:

Hachiya designed the project and is the only pilot to fly the resulting “Open Sky M-02J”. He started with a hand-launched, scale model to test the airfoil characteristics. Once he was satisfied with the basic design, he partnered with aeronautical engineer Tota Ueno of Olympos Company in Tokyo to scale up to a glider capable of carrying one person…Hachiya himself. The glider, first flown in 2006, was launched from the ground by teams of people pulling a bungee cord. Once satisfied with its flight characteristic, Hachiya and Ueno worked to find the “right” engine to add as the powerplant. Between 2010 and 2013, they were doing high-speed taxi tests and working through issues…particularly powerplant and regulatory issues. They ultimately decided to use the NIKE jet engine made by AMT Netherlands which produces 176 pounds force. The jet was designed and mostly used in target drones.

At least the model couldn't be steered by weight shifting, and looking at the harness of the pilot, his capacity for weight shifting is rather limited. My impression is that weight shifting is primarily used for ground control. If you watch the YouTube movie, it becomes apparent that he is barely capable of controlling the direction on the ground, and has to lean to the left on take-off to prevent it to escape the runway. Also, his movements are more sideways than back-and-forth. The control surfaces hardly move, but show linkages on the bottom side, so they are moveable. If you look closely, you can see pulleys on the left and right of the pillow Hachiya-san is lying on, and as @quietflyer says, they should control the elevons, but he adds his weight to help controlling both pitch and roll.
Louise Hose of Kitplanes again:

To date, Hachiya has made about 150 “jump” flights and 70 circling flights. He has flown it up to nearly 500’ agl but believes it can fly much higher. (Airspace restrictions in Japan have prevented him from trying to fly higher.)