Augustus never called himself emperor and none of his succesors did either, so why call them an empire?
Well, "emperor" is the English term derived from the Latin "imperator" which Augustus did use as a title. In Latin it just means something like "successful general" but Augustus and his family monopolized the term.
It doesn't have anything to do with "empire" in the sense of having one state dominating others. Rome had done that since the end of the first Punic war.