We know for a fact that the spiders eat people. This is proven by Omega File no: 7 which says "..whats left of them" its easily the most important lore reveal in the game as it sets the foundation for every other action in the game. This is also hinted at in Spider Noirs description, which says: "She was a real maneater..." (we know for a fact this is a spider). Also in the final-final level Consequences there are a ♥♥♥♥ ton of "PLEASE HELP" "MISSING" "LOST" "CAUTION" "WARNING" posters, the final piece. There are also posters which have images of pets on them, suggesting that the spiders not only eat people, but also creatures. I wouldnt be suprised of one those pets or people were related to the Exterminator in any way. This is also why there are no other people. Everyone has either left or been eaten.

Id like to bring your attention to the Omega Files. These guys are sprinkled around the maps and give you a little bit of lore info. Specifically i would like to present to you Omega File no 7.
The important bit goes as follows:

We found West and Stone, well, whats left of them at least.

This shows that West and Stone (employees of Kill it With Fire) either commited suicide in some horrendously brutal way, or got eaten by spiders. This shows to me that the spiders dont fear Kill it With Fire, atleast until you showed up, which is pretty important.

The Omega Files also show that KIWF created the nuke on Contingency Omega, which shows that they are aware of the spiders, and want to stop them.