The characters are, in fact, Space Opera
adventurers on a quest to save the Green-Skinned Warrior Princess from the Dread Lord Ruuglon.
Dante (in fact, Dantron 3000) has been affected by a malfunctioning Lotus-Eater Machine
, and, as a native of the 13th-century-Italy planet, is experiencing the whole thing as a metaphorical journey through his own mind.
More astute readers may notice that each level of the mountain is really a veiled metaphor for a sin, and everyone who is on these individual levels seems to be suffering for something. It's not a great leap of logic to assume that the suffering is their penance for the sins they committed in life, and they are on this mountain to atone for their sins. Thus, the Mountain in Purgatorio may appear to be a mountain, but is really Purgatory.
Beatrice is actually Jesus
Look at that scene where Beatrice descends from Heaven to great Dante. The angels address her in much the same way that Jesus was addressed when he entered Jerusalem. Also, in the Italian, the gender is wrong.