Too much parsing can obstruct the intent. The “Roman Empire” is a name we give to something. Both Rome and empire can have meanings outside of what is meant by “Roman Empire”.
Is America an empire whether ruled by a dictator or a democracy? And hasn’t “American” civilization become remarkably international?
I use the latter definition I cited early. It is clear that Rome and Great Britain controlled masses of land by conquest way beyond their “normal” borders. And that a few people ruled those territories as well as the home country. That meets the definition of Empire I am using. The fact that some one calls themselves an emperor does not have to be included imo.