Does Lovecraft belong alongside Steinbeck, Fitzgerald, Hemingway, etc. as a literary author? If not, why not?
I would say: definitely not. His style is laughable - his prose overwritten to the extreme. When he's trying to horrify his audience, he keeps describing things as "ancient" and "nameless" and sometimes "eldritch," hitting us over the head with a limited set of adjectives until we're unable to contain our mirth. He had a line in "At the Mountains of Madness" about terrified blind penguins fleeing something ancient and nameless that had me rolling on the floor. He did have his strengths, though. He had a terrific imagination and was a first-class mythmaker. I think that's why people remember him today.
Poe and Lovecraft had very different styles to incite fear/horror/unease. Poe was obsessed with eyes and the fear that stems within someone's mind. Lovecraft, as @minstrel says, was more about the supernatural, not as in paranormal, but what's possible beyond our limited comprehension.
No, he was a genre writer. His prose is often over wrought, but then that kinda goes with what he was writing. He must have been doing something right to have spawned such a legacy. I'd like to do something lovecraftian, but it is a million miles away from my style, maybe some cthulhu erotica...