The ancillary characters of the original film bear an oblique (odd, weird) relationship to the analogous ones mentioned in the novella. I haven't read the novella in many years but it mentions "the Engineer" as a creature in the background, possibly running the whole show, Leviathan-style maybe. The goofy model-thing that harasses Kirsty a couple of times (you can literally see grips' feet pushing the model on wheels if you freeze it) is the stand-in for this.
Then there's the entity that watches over the box. There are three aspects given in the film. There's the asian guy in the market, the hobo, and the "final form" skellington dragon that picks the box up out of the fire and whisks it away. Perhaps they are all the same entity, or perhaps the one is the dog/gofer of the other?
I don't think they're (it's) cenobites, though, but perhaps a lower form(s) that just keeps the game going. You may be getting the Devil himself idea from multiple tropes: the devil is popularly depicted as a "dealmaker", and the film opens with a deal. Also, the hobo wanders the earth, just as Satan is supposed to do. Also a winged skellington-dragon is a convincing final-form which evokes Satan via Baphomet imagery, true form as a Beast, etc.
For these reasons, I did personally have a vague idea to myself that this character was/is the Devil, like you, but on repeated viewings that's not quite right, I think.
I think that these aspects are suggestive of The Devil Himself but not literally such.
hellraiser.wikia.com/wiki/Derelict,_The_Puzzle_Guardian
The real purpose of the character is to mysteriously suggest that there is a whole evil infrastructure keeping the whole game going, periodically fishing out fresh new victims, down to a science. It's also a cute way to assure the possibility of a further sequel, like any given creature coming back to life/opening its eyes in the final scene, but less hokey.