Why is atom not a perpetuum mobile? Why is perpetual motion and interaction of elementary particles (not) considered a perpetuum mobile? In the broadest possible way of thinking about it.
Physically, there's nothing wrong with being perpetually in motion. It is consistent to have an electron with angular momentum about the nucleus for an infinite amount of time and I would call such a thing in perpetual motion.
Likewise, if nothing were in the way such as other planets (or if the sun did not go supernova) or whatever, the earth would revolve around the sun forever . It is in perpetual motion about the sun.
One more example: A cannonball shot off into space at above the escape velocity of the earth sun and milk way will almost certainly be in perpetual motion unless something gets in it's way.
However, in all three of these examples, you are not free to harvest infinite free energy from these things for reasons that should be intuitive to you in the case of the earth and the cannonball. If you were to harvest energy from the earth's orbit you would shrink it's orbit, eventually causing it to fall into the sun. There is a finite amount of energy stored in it's orbit. Likewise, there is a finite amount of energy stored in a cannonball at some speed and once you harvest it all, it will be stationary in your reference frame. These arguments gain some nuance quantum mechanically, but ultimately are the same. There is a finite amount of energy stored in an atomic orbital.
As was pointed out in the comments, I was ignorant of the actual definition of a perpetual mobile. So in the end, no the atom is not a perpetual mobile, even if it is perpetually in motion.