Well, this is a form of rotary engine, quite similar to the Wankel. It is possible the manufacturer's claims are valid, but even if so, I see a few disadvantages.
First off, of course, will the rules allow a rotary engine? Secondly, we already have the Wankel, which is now very well developed, puts out respectable power, and reliable.
So I make comparisons between this new quasi and the Wankel.
The quasi promises a continuous burn, without the need for spark plugs once idle is achieved. OK, maybe possible, but hey, having a spark plug isn't such a bad thing, especially since the quasi will still need a spark plug and associated equipment anyways, just to get it to start.
The Wankel has a one piece, solid rotor, while the quasi has a rotor consisting of a lot of moving parts. Personally, I like as few parts as possible, I consider them as just increased the likelyhood of something breaking.
I have scoured the quasi web site looking for direct comparisons between them, and although a lot of comparisons were made, very little numbers were mentioned. The best I could dig up was 14 HP and 25 ft/lb at 3000 RPM, from 200cc aspirated volume. This was calculations, with no real real world testing to verify the claims. Also, this was back in 1999, so I expect that in the six years of development since then, we should have seen an engine that should have matured and produced better power and reliability. But all I see are claims, and not much else.
It's a nice, and novel concept, and maybe one day could see large scale production. But until I see valid numbers, real world dyno results, this sceptic will stay with what works.