Since the realm is the Prince, then if the Prince manifested on Nirn, wouldn't s/he still be a god? Sure, there are heroes and servents, and even some talking statues, but I'm talking about a real manifestation of a Prince, like how Mehrunes Dagon appears several times to stomp around on Nirn, or when Azura appears ('cause she knows the secret to bypass the Lunar Lattice).
Dagon only appears in special cases (Like when Aedra and Daedra are actually nondistinct because Oblivion and Mundus are nondistinct) and Azura is not absolute on Mundus. Like Prow said in the Lore section response, the rules are different for spiritual beings. The Prince is his/her realm, but they are only their realm. The bearded jolly lunatic isn't Sheogorath, the Isles are, any appearance on Nirn is just an avatar they choose to take, and since it is an avatar, a false, illusory and fleeting projection of their will as best it can be manifested, it is finite and therefore not a god. Mundus is one-eighth of each Aedra, thereofre each of them has one-eighth of absolute power. And while the power of a prince Avatar is far beyond any human, it is nothing compared to one eighth of the entire planet's power.