I get the intake, compression, and ignition. I can see how a "pressure wave" could accomplish the compression function. What I don't see is the explosive force moving anything, except for maybe exhaust escaping the chamber on blowdown (which doesn't strike me as efficient but what do I know?)
If it does work, it is said to be a very high rpm, very low torque device, not suitable for direct mechanical connection to the wheels- which is fine if the system supports that.