A Physics Constraint with an Angular Motor will essentially spin, but the detail is in how it spins. An angular motor Driven by Velocity will apply a constant force to essentially "spin," where as a Driven by Position will attempt to obtain an angle based on the size of the spring and dampening applied to said spring.
Also what may not be completely clear is that the constraints themselves are actually what is spinning, not the objects, but since one of the objects is not simulating, it forces the other one to move. Try enabling Simulate Physics on the red cubes to see how it flails around.
Enabling Simulate Physics on the red cube will cause it to travel around the room.