My understanding of detonation is the simultaneous, uncontrolled burning of fuel throughout the charge volume.
In an internal combustion engine, detonation, (heard as a tinkling noise called pinking), will cause damage - what is desired in the IC engine is a travelling wave front that moves across the fuel charge at the right time in the cycle, providing a progressive pressure increase.
With the engine of this thread, there are no pistons etc to damage by detonation of the fuel. However, if more fuel is being continuously fed into the combustion zone, then this seems less detonation and more travelling wave front to me.
In fact the engine looks like a rocket engine to me - the differences being that :
a) hot gas is injected into the (second) combustion chamber rather than pressure fed oxygen and fuel, and
b) there is an obstruction in the exhaust nozzle.
The increased exhaust gas pressure around the obstruction might be adding something, but it is not clear to me what that might be. Perhaps the turbulence caused by the obstruction burns off any unburnt fuel, thereby increasing power and efficiency?