It might sound a silly name, but I remember it was quite a revolutionary (no pun intended) design...
IIRC it has fewer moving parts overall, better power transmission efficiency etc. The only stumbling block as I remember was the seals on the 'cam' (not sure what the correct term for the rotating doobrey that replaces the piston is). The materials available at the time weren't up to prolonged use, gradually wearing away and causing the thing to break down. Presumably modern materials have solved this.
Doesn't one of the newer Mazda's use a Wankel engine? Except it is now called Rotary. Presumably the marketing people thought "Wankel" was not going to sell.