The engine in the video is not a Mazda and is not of Wankle design. It is a complete new engineering concept.
Ok, Herr Wankel invented the eccentric shaft rotary internal combustion engine. The liquid piston engine is an eccentric shaft rotary, i.e. "Wankel" engine. Not "Wankel designed", as the good man has been dead for nearly 60 years. As such, the "liquid piston engine" (I'll take "bad marketing names for 400", Alex) is an incremental design improvement, rather than a "complete new engineering concept".(I'll take "bad marketing hyperbole for 200", Alex).
The biggest differences are the multiple firing points during the cycle and the intake and exhaust port location. These seem to address two of the four or five primary problems with Wankel engines: 1) uneven heating compromising seals due to the combustion taking place at one side of the engine, only, and 2) poor thermal efficiency of the engine due to unburnt fuel washing out of the exhaust port (even though "shooting dragon flames" is quoted by rotary engine fans as one of it's most endearing qualities.....).
The problems of seal wear / maintenance, the need for using oil in the combustion chamber to prevent that seal wear, and the emissions problems resulting from that oil consumption are not specifically addressed, which concerns me.