The poem has characteristics of a simple ballad, particularly the first four lines of the poem, which follow the abab format and the lines have alternating three and four stress lines (called "ballad meter").
It has a sing-song quality to it and tells a story -- two characteristics of any ballad. The rhyming scheme is fairly simple and repeated as well.
In the fifth stanza, Poe breaks out of the 3/4 foot lines, when he adds an extra three-foot line:
“Of those who were older than we—
Of many far wiser than we—.”
Given these characteristics, I think you could safely say it could be considered a ballad.