She's the head bitch in charge in Dryl, making her the ruler. She goes by Princess without a hereditary monarchy, because Empress Entrapta isnt quite as friendly sounding. Of course if anyone were to threaten her rule, she has an army of killer robots and Hordaks to defend her sovereignty.
Actually, I wonder if her kingdom is super young, being established after the war. Unless it was a kingdom ruled by sentient robots who adopted a human with unique powers, but I doubt it because its implied that she built her robot parents. Seems like the only tech based kingdom with a shaky government would have been a priority target for the Horde early on.