The Dovakiin and the Thu'um may be important to Nord culture but they do not "belong" to the Nords, they "belong" to the Gods who created all of the beings that inhabit Nirn. This should be obvious by the fact that any race can be Dovakiin, seemingly chosen by the Gods themselves, and that anyone, with intense training can learn the ways of the Voice. It may be weird to you that an Argonian or Khajiit can be Dragon born, which is looked on upon as a human concept but you must look at it from the perspective of the world in which they exist.
Daedra are not gods, they are god-like beings in the realm of Oblivion. Dunmer were created by Boethiah and Orsimer were created by her devouring of Trinimac, who then became Malacath and transformed a race of Mer into todays Orcs. Khajiit were wood elves that were cursed and Argonians came from a dinosaur-tree.
That, IMO makes the role of Dovahkiin only fillable by (in descending order)
Nord
Imperial
Breton
Redguard (MAYBE, as their lineage is completely detached from the other races of Man)
I don't understand how an Altmer would be Dragonborn nor a Bosmer, but this is just my opinion and it is possible to roleplay any type of Dovahkiin, which is good, as there would be some meg nerd-raging if you could only be human (I'm looking at you, BIOWARE!)