For me, the Svart are clearly drow, or at least they were designed with the drow in mind (as well as the Winter Court, of course. That's also why I'm not so fond of faeries). : most of the units are female except for workers, they favor Esus (deception, treason, manipulation), etc ...
They don't have innate magical abilities, true, but I just take that in as "Our drows are different". After all, Our vampires are different, so why not.
The spider thing is mainly religious, and the religious aspect is covered with Esus, so there. Maybe it would be possible to give them a more "Underdark" vibe, but I'm not even sure it's necessary.