On further inspection, I see they are judt running a recuperator. You could do the same thing by taking a V8, using 4 pistons for compression and 4 for 2 stroke combustion with a recuperator. You'd end up with the same problem, one hell of a lot of heat.
From their website:
To create an even more efficient engine, atomized liquid water can be sprayed into the compressor inlet to keep the compressor cool. Keeping the compressor cooler allows compression to be more efficient thus the engine will be more efficient.