"motorcycles have no motors?" ? WRONG
"motorized bicycles don't have one either unless they are electric" ? WRONG
A device is a constructed tool.
A motor is a mechanical or electrical device that causes a rod to rotate. All motorcycles and all motorized bicycles have motors.
An internal combustion engine is a heat engine (itself a subsystem) used to do mechanical work. This work almost always involves turning a rod.
OP, I totally understand your freethinking, but your argument using very weak semantics like that is a bit amateurish.