I think there should be a cut off point for cultural spoilers of this magnitude. If it was five years ago, I think we can move on and say that if anyone hasn't read it by now, it's their own fault.
Yep, that''s how I feel about it. To me if it's been out for a year, it's open game. Seriously, if you wanted to read/see/play it you would have by then.
Anywho, I'll tell you what most think it means. Your character assumes the role of Sheogorath and eventually becomes him.* To the mortals of mundus there is no noticeable difference.
*Considering what Jyggy says to you at the end I'd say it's certain. The Shivering Isles literally belong to you. You rule over a plane of Oblivion. If that wouldn't make you a Daedric Prince eventually I don't know what would. And when you take into account some of the new lore brought it by SI it hints at the possibility that other champions have came and assumed the mantle (Arden Sul in particular) though none have actually broken the cycle until you.
Obviously they couldn't make you a full on prince at the end of SI because you wouldn't have been able to ever re-enter mundus. And people would have complained about that. A lot.
Edit* Plus it's not like a mortal becoming a god isn't unheard of in Elder Scrolls anyway.