Paradiso, like Inferno and Purgatorio, is an epic poem. We know it's epic because we're talking about larger-than-life topics, like how the universe is organized, what is the best use for art, and the salvation of man's immortal soul. Got the "epic" part?
If not, remember all the invocations to the muses, epic similes, and famous people? That's all characteristic of epic works. The "poetry" part is pretty obvious. It's written in verse; it has a meter (a special thing called terza rima).