No ... no ....
The origin of the Falmer was explained. They are not Goblins. The game programmers may have used some similiar behavior program modeling code, but that's it.

Personally, I'm convinced that Goblins are yet another monstrous branch of the Meric branch of the Ehlnofey family tree. Orcs were revealed to be Orsimer. Falmer were degenerated under conditions of slavery. Khajit, according to their own lore, share ancestry with the Bosmer. Dumer are, themselves, changed from the Chimer. In Tribunal, it was revealed that the Altmer often use Goblins as troops, that there is some kind of relationship between them. Elves just seem to be so malleable (both in TES, and in other fantasy mythologies, with the Elf/Orc connection going all the way back to the original source for both races in their modern form), it's easy to imagine Goblins are yet another kind of Elf.