Having done that, they created what is arguably an Empire
The term empire does mean a set of captive nations ruled by another nation -- it doesn't matter what that ruler nation's government is.
Note that also there were Emperors (or specifically Imperators i.e. Military dictators/commanders in chief) right from the early days of the Republic.
Augustus didn't establish the Empire, he established the position of Princep (first among equals) that was kept until Diocletian started the Dominate period
I wish SunkenCiv would come back.