Rather than have one big continuous burn, the rocket engine rotates to create many small burns, by mixing and igniting small amounts of two gases at just the right frequency and amounts. This apparently leads to a more efficient conversion of chemical to kinetic energy.
This sounds similar to how a car engine uses a fuel injector to inject then burn small amounts of fuel to make the pistons go.
Instead, the fuel mixture ignites in one spot, and the explosion spreads at Mach 5 around the engine but once it reaches the end of the combustible fuel, more is injected behind it so the explosion can just keep traveling around in circles.
Judging by the article they managed to get that working, and also came up with a better way to take videos of this happening (high speed camera, tracer chemicals in the hydrogen, better signal strength).
I'll link directly to the transition part:
IIRC they dropped that early on as well.
« rotating detonation rocket engine»
« The rotating detonations are continuous, Mach 5 explosions that rotate around the inside of a rocket engine »
maybe like a wankel engine without the rotor?