From the livescience article linked by another poster: biofilm produced by sulfur-eating bacteria, which in turn metabolize sulfur from the sulfur-rich stream in the cave.
So the whole food-chain here is: sulfur -> bacteria -> midges -> spiders.
> The environment, too, is unusually protected. The cave is hard to reach and is filled with foul-smelling hydrogen sulfide gas, in concentrations too great for most animals to live there.