A few basics for clarification
Shockwaves are the best way to achieve efficient compression _of_anything_ as has long been known. Higher compression (and expansion) is the key to getting higher efficiency. That this turbine might reach 60% efficiency of thermal energy conversion is not putting it beyond Carnot efficiency, but such high pressure & high temperature combustion could lead to high levels of NOx (nitrogen oxides) emissions IF the gasses remain very hot and very compressed for an extended time... which they won't! That's another beauty of this beast: the combustion and expansion in each chamber will be all over in a few microseconds.
My only gripe at this stage is that this video needs to be subtitled, as he seems to switch to speaking German in a few spots. Even so, I *could* make out the power output figure he stated: "25 kilowatts", which equals 33 and one-half horsepower. Still plenty to get you down a level road at legal speed... even with the A/C on. [1 HP = 746 watts]