I am not able to reconcile what D&D really means by "race", other than the tables of abilities in the player's handbook.
The basic biological taxonomy goes as follows: kingdom, phylum, class, order, family, genus, and species
Then where do Tieflings branch away from humans? They seem to have a spinal cord, so the phylum "chordata" is the same. I would guess they could be considered mammals? But on the other hand, maybe they could actually be in a different class. Once again, the virtue of unknowing reveals itself.
The term "race" is certainly misleading. As you suggest, "race" exists merely as a mechanical construct in DnD, at least for player characters.
With a few exceptions, all available player races are classified as "humanoids" and among those, almost all of them can interbreed. In biological terms, it'd make sense to classify them as part of the same genus. From there, it gets tricky, because magic enters the equation. Tieflings are, for the most part, humans, whose bloodline got changed by fiendish essence.
