In the case as shown in the youtube clip, rotation of one of the magnets around its rotational symmetry axis  won't induce any motion of the other magnet. The reason is that the magnetic stray field itself has rotational symmetry. Thus, the rotation does not lead to any spatial change in the stray field of the rotating magnetic. The other magnet does therefore not experience any force. Magnetically actuated rotation of a ferromagnet requires a change in the surrounding magnetic stray field. Rotation is induced if the orientation of the stray field lines changes (torque). Hope that answers your question.

Thanks !

The Video also shows, that here is no stable magnetic levitation  possible in this arrangement unless you fix (strap) the magnets in order to prevent them from moving radially or from flipping over.

But, in a ideally configuration it can be done isn't it?

No it can't! !

I suggest you look for "Earnshaw theorem"

For levitation, a minimum in the local  potential is required. such that the magnet gains energy when moving out of that local minimum. Since the superposition of the gravitational field and the magnetic field does reveal only saddle points but no local minima, there will be always at least one direction where the repelled magnet will move to in order to find a lower energy state.

Ok, thanks again, totally agree!

One more word about 'ideal configuration'.  Yes, it IS possible, but in fact this situation closely resembles vertically positioned pencil staying straight on its tip.  Arbitrarily small disturbance will destroy this effect, just because - as Manfred already said - the pencil is not in its potential energy minimum but rather at maximum.  The only uncertain/unpredictable thing is the fall direction, due to perfect symmetry.

I feel that static magnet must have influence in the ration of an magnet. The influence depends on location of the poles of the magnet and the strength of the static magnetic field. If is very small compared to the strength of the rotating magnetic field, one can neglect it. However, the strength of static magnetic field is compatible to that of the rotating magnetic field one cannot neglect the earlier.