Was Jack possessed by The Hotel's ghostly supernatural evil? Or did he become insane?

In the book, it's clearly the hotel bewitching/possessing Jack to kill Danny for his "shine."

Kubrick made that point much more ambiguous, except who/what let him out of the pantry?

I've never read the book, but in the movie it did seem open to interpretation.

I'd say it's more the Ghosts caused him to lose his sanity

i think it's both. He is being corrupted throughout the film by the hotel. Mostly insanity i guess.

Is it possessing him though? Possible.

He is in the picture at the end of the movie. So, the hotel and its "energy" was possessing and absorbing him.