Since the "clutch" only applies torque in one direction, as soon as the engine turns over, the starter can just be pulled off. As for the actual connection, I'm guessing it's just some sort of spline.
FWIW, I start my B&S lawn mower engine with my power drill ala the racing starters you speak of (very old mower - starts hard). I cut the rope recoil mechanism and a 7/8" 12-point socket fits right on the starter clutch shaft. Spin up the drill, and once the engine's running, I just pull the drill off. However, if for some reason it doesn't fire up, there's a hell of a kick-back, if I leave the starter (drill) on too long.