I also think it's instructive to look at that word "natural" in the "natural" and "empty" desires.
Natural is φυσικός "physikos" "natural, produced or caused by nature, inborn, native."
The natural desires are the ones that we're born with, the ones that naturally arise because of our being physical, material, mortal beings.
The "empty" desires then - to me - refer to desires that have been inculcated in us by culture, indoctrination, societal expectations, etc. They do not naturally arise within us. They are desires we've been taught that we "should" have -- lust for power, greed for unlimited wealth, etc. -- but that can never be satisfied.