Does a card moving from Exile to Exile count as being moved?
Hallowed Moonlight instructs you to exile. This is what the replacement effect in question replaces.


  903.11. If a commander would be exiled from anywhere or put into its owner’s hand, graveyard, or library from anywhere, its owner may put it into the command zone instead. This replacement effect may apply more than once to the same event. This is an exception to rule 614.5.


As such, you may indeed return the Commander to the Command zone, even if the instruction would otherwise have done nothing at all.

As confirmation, 406.7 does presume than an exiled object can be exiled.


  406.7. If an object in the exile zone becomes exiled, it doesn’t change zones, but it becomes a new object that has just been exiled.