The Inferno is in verse. It rhymes. And has a meter (a fancy meter called terza rima). Do you need any more convincing that Inferno is a poem?
As for the "epic" part, Dante is talking about a man's choice between good and evil and showing us the eternal agony of those who pick Door #2. For you skeptics out there, you know it’s an epic when you see big long epic similes every fifth line. Take into account the fact that Dante is guided by Virgil, the epic poet of Rome, and you’ve got yourself an epic poem.
Oh yeah, and Dante invokes the Muses. When you have Muse-invocation, you know you're dealing with an 100% Grade-A Prime epic.