Into what genre do both Edgar Allan Poe's "The Philosophy of Composition" and Stephen King's On Writing fall? fiction nonfiction drama poetry

'Nonfiction' is the correct answer, because this is not fiction, a work of art. Those are theoretical essays, where they talk about how poetry/prose should be written. They aren't dramas, and certainly not poems.

The correct answer is nonfiction.

Both of these texts are theoretical essays on writing and what constitutes a good, academic text. Essays fall into the category of nonfiction, which is why fiction is the incorrect answer here. Both of these are texts, essays, and not poems or plays, which is why those answers are also incorrect. The texts deal with what the writers can do to make their writing better.