Your definition of a solenoid is correct except it forgot that moving a heavy duty electrical contact is a useful mechanical part. It's usefulness is that the contact can easily carry the large amount of current the starter motor requires.
Actually, while on the subject, the old automotive starters that had an attached solenoid also had a similar heavy duty electrical contact built into them.
When they were actuated they moved the gear into engagement with the flywheel.
In the last little bit of this movement they engaged the electrical power to the motor.
As for the Royal Enfield, its starter is always engaged with the gear train that drives the sprag clutch.
When the engine is off and the starter soleniod sends power to the starter motor, the motor starts to run turning the gear train and the sprag clutch.
If the clutch is working properly, its sprags will lock up on the crankshaft transmitting the starter power to the crank.
When the engine starts, the crankshaft is turning faster than the sprag clutch so the sprags loose their grip.
As the electrical motor is turned off (solenoid is d-energized) the motor and its driven gear train stop moving. The spinning crankshaft continues to "run free" under the sprags and you ride away with a smile on your face.