This is more hype than performance.
When I worked on a hybrid-power multirotor drone about eight years ago, I was checking out Wankel engines for their power-weight ratio, and also came across this Liquid Piston crew. They were supposedly ready to ship Real Soon Now. But worse, their power-weight just didn't compare to Wankel options available then.
Liquid Piston still do not compare on their headline power-weight ratios. They make a lot of claims about 25 HP (18.6kW) and light weight, but don't actually mention the weight, which is down in their spec sheet - 21.2kg dry [0], which is about 0.877kW/kg.
By comparison, just a quick search of small Wankels turns up these:
-- AIE model 225CS outputting 40 bhp / 30kW weighing 10kg = 3.0 kW/kg[1]
-- AIE model 80S outputting 15 bhp / 11.2kW weighing 5kg = 2.24 kW/kg [2]
-- Sorrel Hiperlight Wankel outputting 75 hp / 56 kW weighing 52kg (fully wet with all electric start, reduction drive, and exhaust system, etc. = 1.07 kW/kg [3]
-- Crighton CR700W motorcycle engine puts out 220 hp / 164 kW weighing 43kg = 3.8 kW/kg. [4]
-- Small Nitto NR20-EP puts out 2.24kW / ~3hp weighing 1.466 kg = 1.53 kW/kg. [5]
In short, this is a lot of marketing hype for low pefrofrmance, and they've been working on it since 2003 according to their website.
The sole advantage this engine might have is running on a broader range of fuels including JP-8, but I've seen Wankels setup for a wide fuel range also. If I had a funded task to develop a high power-weight engine, I'd start with the Wankel design, not this one. It is already WAAAY ahead, and there's still a lot of performance left on the table.
[0] https://uploads-ssl.webflow.com/5f6086e9bbbabd41a20f2984/642...
[1] https://www.aieuk.com/225cs-40bhp-wankel-rotary-engine/
[2] https://www.aieuk.com/80s-15bhp-wankel-rotary-engine/
[3] http://www.ultralightnews.com/sunfun99/hiperlight.html
[4] https://newatlas.com/motorcycles/dual-rotary-crighton-cr700w...
[5] https://barnardmicrosystems.com/UAV/engines/wankel.html