I don't know if Demons need worshippers per se, the fact that Demon Lords are respected and feared by thousands (often millions) of lesser demons might provide the same general effect.
My personal game theory is that Demons are composed of
Plasm, like ectoplasm except in this case it is a wholely detached substance generated by the Demonic entity as it's physical body.. thus demons can have seemingly outlandish physical forms and may exist without need of internal organs or even the need for food, air, or water.. they can also exhibit the capacity for huge excess.. eating constantly, constantly bleeding, expelling noxious gases..
Since plasm is, like ectoplasm, a psionically based material, it follows that it and the entities who make such vital use of it, are receptive and responsive to mental energy.. worshippers act as psychic boosters to the plasm form, providing more energy and vitality to the Demon because it no longer has to devote mental energy to keeping it's form coherant.. worshippers take care of that for it.. instead it can devote it's psychic potential to other things, such as gathering magical or psychic power, and eventually, the god-like powers of a true Demon lord.
That's just my theory on it all and is not based on any official rules, though I think it fits the theory behind the rules quite nicely.