Does this mean the Galactic Empire and the Imperium of Man are also not empires?
It's almost harder to define what the core of the Galactic Empire even is. We are told Coruscant is core to the Empire, but the glimpses of it in the Old Republic era certainly implied it was a very diverse place and we aren't really shown Coruscant in the films of the height of the Galactic Empire. To some extent the only truly "core worlds" and "core peoples" that we see in the films are the Star Destroyers and Deathstars, the military demanding taxes from every planet they pass.
The Empire may not be taking full advantage of the military power of a diverse people because of the over-reliance on clones and treating draftees as if they were clones when the clones start to run out, but beyond that it certainly seems to resonate like an Empire in the way this article describes an Empire to me.