Good point that bore repeating. Pulp certainly refers to the original magazines, which Lovecraft's work appeared in. Which means that by that definition, Cthulhu = pulp.
Doesn't invalidate anyone's choice to play games in whatever style they enjoy most. Personally I think Indiana Jones or Buck Rogers or Barsoom when I think of pulp. But if I put Shub Niggurath into the town square, I'd expect there to be a sanity reaction from the protagonists. Not from seeing a mi-go, unless you were Indiana Jones. Because Buck would have seen aliens, and Barsoom already contains various types of monsters. But Indy should, IMO, have a sanity issue from the mi-go appearance. And again, I would have him gibber, and then grab the dynamite. The story must go on, after all...