They seem to be literally patterned after the Romans. Their home planets are called Romulus and Remus-- the same as the mythological founders of Rome. What a coincidence! Lol
Their soldiers are called centurians, they call themselves an empire. Even their hairstyle resembles the ancient roman style.
It was way too obvious they were meant to represent a menacing empire to the Federation.
It worked in TOS, but TNG toned them down and they seemed more like the mustache twirling villains trope.
Power and military wise, the Dominion appeared the most Roman-like.