The 'how it works' page states: "While it is a rotary engine, LiquidPiston’s X Engine is NOT a Wankel engine. It has a fundamentally different thermodynamic cycle, architecture and operation."
But it doesn't really state what is revolutionary. And when I hear rotary engine, I immediately think about sport car engines like the Mazda RX-8. Great for a fun car with smooth power delivery, but it needs tons of revs to perform (some RX-8 engines deliver peak torque at 5.5k rpm and power at 8.5k rpm) and are not economical at all (and thereby efficient).
I'm sure it can live up to the compactness factor to some degree; because it basically fits 3 cilinders around a rotating cilinder+crankshaft. One issue I think however is the geometry. If you decide to build a larger engine (e.g. 1.5L for a road car), you need to fit 3 large cilinders. The way those inlet/outlets are drawn makes it harder to build a 2-rotor design. The only way is to then go out in width/height, which is unpractical. It also needs a good bearing and seal between gasses and the crankshaft.
I believe the RX-8 wankel engine is also loved because you can mod it to a 3/4-rotor rebuilt design. AFAIK you can even reuse many parts of the original 2-rotor design, as it's quite a modular block.