I don't know the specifics of the RE starter/sprag but in general the gears from the starter need to kick out and engage the flywheel to start and engine. Once started they retract. The gears here seem to be stuck engaged, that's why the starter turns over when you kick it, turning the engine over.
My guess would be the sprag clutch since I think that's the mechanism involved here. It may also be something with the relay. Give the relay another solid rap with a mallet or whatever and see if it works.
Scott