Short Answer: Yes
The dark Tower is the work that connects all Stephen King works
I have written enough novels and short stories to fill a solar system of the imagination, but Roland's story is my Jupiter--a planet that dwarfs all the others . . . a place of strange atmosphere, crazy landscape, and savage gravitational pull. Dwarfs the others, did I say? I think there's more to it than that, actually. I am coming to understand that Roland's world (or worlds) actually contains all the others of my making...
Specifically about the relation between the shine and The Shinning: Jake Chambers (from the Dark Tower) has psychic powers, refered as the Shine, that are similar to those of Danny Torrance (the little fellow on the trycicle that found two charming sisters in a hotel hallway). Danny's powers are called in similar terms:
"You shine on boy, harder than anyone I ever met in my life. […]. You got a knack. […] Me I've always called it shining. That's what my grandmother called it, too. She had it. We used to sit in the kitchen when I was a boy and have long talks without even opening our mouths"
In other King’s novel The Stand, prophetic visions are said to be
“the shining lamp of God… sometimes just the shine.”
So it seems King is kind of using the shine as a common term for this psychic powers across his universe.
On anoteher note, Jake and Danny are possible twinners: different versions of the same person, living on different levels of the Tower.