Can "The Open Window" fall into the category of horror?Hi. I have to compare this story to another horror story. Can I say that this story is a...

You are correct that "The Open Window" by H.H. Munro
(known as Saki) contains elements of both humor and
horror.

The story of fifteen year-old Vera "putting one
over" on the nervous Mr. Nuttel is clearly the tale of a successful practical
joke.

On a deeper level, however, the story is about the
fine lines that separate reality from illusion and sanity from insanity.  Vera's story
is in many ways perfectly plausible: hunters sometimes are killed, and their families
sometimes irrationally wait years for them to return.  Mr. Nuttel is certainly a nervous
man, and it is not surprising that the apparent realization of Vera's story is enough to
push him over the edge to insanity.

These "games" of
reality/illusion and sanity/insanity are standard tools-of-the-trade of horror writers.
 They create monsters that are just a bit more frightening than many real-life dangers
and they push their characters over the brink of sanity.

In
this respect, "The Open Door" can be considered a horror story.