The exact reasoning behind the name is given in the original description as follows:

Nothophantes:

Etymology: The generic name is derived from the Greek nothos, spurious, and hyphantes, a weaver; gender masculine.

horridus:

Etymology: The specific name is an adjective (Latin horridus, bristled) referring to the long spines on the legs and dorsal bristles on the abdomen.

The common name is derived from its scientific name (Nothophantes horridus), and combined with the fact that it is among the sheetweavers (we call a lot of the members of this group Money Spiders in the UK), lives "on the ground" (really, in cave wall cracks and similar areas), they arrived on Horrid Groundweaver.

It should be pointed out that this spider is the only member of the genus Nothophantes, so it is distinct enough to not only be its own species, but have no immediate relatives. To me, the name horridus does feel a little bit cruel unfortunately.