The story is set, though not explicitly, at some point in the middle ages, evidenced by the name of the prince: Prospero, yet the narrator does appear to be speaking from a point in the 19th century, and speaking as if to an audience.
The narrator, who several times presents himself or herself as an aside to the reader—’but first let me tell you of the rooms’ (687); ‘as I have told you’ (689) and so on—and who somehow or other seems miraculously to have survived the Red Death in order to be able to tell the story, presumably was an eye witness. How could an eyewitness have survived to tell the tale, and reference a play that was not published until the 19th century?
The only plausible answers are an artificial omniscient being (unlikely, considering this would be the only of Poe’s work to display such a writing style), or the narrator is death himself, personified.
In light of this, I believe the former suggests the piece should be read as both a ghost story, meant to frighten with the idea that death immemorial has harvested the lives of an entire party and has spent the time to recount it, implying the inevitable end of life and eternity of the reaper, and also as a commentary, satirical or otherwise, on the folly and religious fervor of man.