Even before we see the forty-year-old corpse of Homer Barron rotting into the bed, the creepy house, and the creepy Miss Emily let us know that we are in the realm of horror or Gothic fiction. Combine that with a southern setting and we realize that it's not just Gothic, but Southern Gothic. The Southern Gothic genre focuses – sometimes subtly, sometimes overtly – on slavery, or the aftermath of slavery in the South. You can definitely see this in "A Rose for Emily."
Since author William Faulkner won the Pulitzer Prize for fiction twice (first in 1955 for A Fable, and then in 1963 for The Reivers), and the Nobel Prize for Literature (1949) we'd also have to put it in the category of "Literary Fiction."
Even if Faulkner hadn't won all those prizes, we'd still put "A Rose for Emily" in this category. The story is masterfully told, and it's obvious that much care and skill went into it. It's also strikingly original and experimental in terms of form. This is part of what makes it a classic Modernist text. The Southern Gothic is a perfect field on which to perform a Modernist experiment. Modernist is all about what happens when everything you thought was true is revealed to be false, resulting in shattered identities. Modernism tries to make something constructive out of the pieces. We can see all that loud and clear in "A Rose for Emily."