rotary engines have proper 4 strokes - its just the design that allows each face of the rotor to be going under one of the cycles at any given time.
hence when the rotor spins each time a rotor face is facing the plug - there is compressed air mixture ready to be ignited while the one after the plug will be exhausting and the one before the plug will be on intake.
rotary bikes were made - they were too thirsty for fuel and ran quite hot too and were not so good on reliability under the hands of regular motorcyclists.
heres a norton from the 80s
suzuki were also in the game in the 70s with their RE5
btw - There is an old man in North Nazimabad Block B who has this model suzuki RE5 motorcycle - it sounds nothing like a motorcycle.