The series establishes demons (at least the grunts, anyway) were all originally normal humans, and that Hell's hierarchy operates on a Might Makes Right kratocracy. Eric (Ruler of the Treachery Circle) tries offing the actual Satan, only for Kip (Ruler of the Gluttony Circle) to off Satan by pushing him into the same sludge that Eric was sent into, becoming the new Satan in the process. It is possible that the archdemons that rule the circles were all humans at one point as well before they climbed the ladder and found ways to kill (or some other unfortunate fate) the reigning dukes of their respective circles and become co-rulers of Hell. "Darren Farley" and "Eric" do not sound the least bit Biblical, and their accents are very American, so it is likely that they were humans in America at one point.
Being a torturer for a Big Fun kid-at-heart like Gary can be an especially cruel thing to do to him, but it is established that he is much more of a hinderance than he is in actually doing what he is meant to. He is Too Dumb to Fool, too nice to put any real effort in actual malice and has an attention span too short for any torture to afflict any permanent mental trauma. It is established in "Torture" and "Eddie the Demon" that he could easily demote and promote tortured souls and demons on a whim if he so choosed.
Darren is established as being a purposefully Bad Boss. He assigns his workers grueling and unfair tasks. If the demons fail, he tortures them. If they succeed, he tortures them. In "Circle Jerk MCMCVIII", it is established that the real Satan is also a massive dick to his own underlings, he and Eric changing Darren's topic of discussion from "anal torture" to "radical Islam" last minute and changing the time from a few hours to a few minutes, all the while having made up their minds to have the Miscellaneous Circle flooded by the Treachery Circle against his will, Darren clearly too afraid to put up any meaningful resistance. It is even established that the Miscellaneous Circle is essentially unneccessary compared to the rest of the circles, making Darren the "Gary" of the arch demons.
Is it out of the realm of possibility that Satan put Darren in charge of Gary with no real say in the matter just to make his job harder?