Gothryd isn't an elf. His dad was shagging an elf, but Gothryd's mom wasn't an elf.
Plus Aubk-i's marriage to Gothryd was an arranged one, among the peace terms following the War of Betony. Their marriage, if I recall by dialog from Prince Lhotun of Sentinel, helps to cement friendship between the two kingdoms.
Gothryd would probably be a Breton, but there's slight reason to believe he may actually be of the dragonblood. An agent of the Underking says at one point during the main quest, when regarding King Lysandus, that
"not even death can hide a true descendant of Tiber Septim from the Underking" or something. Since the Underking is Zurin Arctus, Tiber Septim's battlemage (more or less), this may be more than a fancy metaphor.