From his entry in wikipedia, it seems that he is not a supernatural character, just a recurring villain, in spite of him being described as
"an accomplished sorcerer and a devoted servant of the Outer Dark", with supernatural abilities involving necromancy, prophecy, and influence over animal and human behavior. His goals typically center on bringing down civilizations through destruction and conflict
It seems that he learned these magic abilities, not that he was born with them due to some sort of supernatural origin (like being Satan or some sort of evil spirit).
Walter learned the ways of Dark magic and became a very powerful sorcerer and to some extent becoming a sort of Demon with a "quasi-immortality".
Remember that the Dark Tower series
connects different worlds/universes/Stephen King's works.
(that explains him appearing in other of King's works such as The Stand or The Eyes of the Dragon)
In this series he
tries to keep protagonist Roland Deschain from reaching the Tower (the linchpin of existence) so he can claim it for himself and become a god.
but he does not have a supernatural origin.