One more point in favor of the story being a parable, aside from those above, is that it contains internal self-interpretations which are unlikely in a straightforward recounting, but perfectly sensible as one of Jesus' self-interpreting parables (other examples are the Wedding Feast and the King's Far Journey, but the other parables in Luke 15-16 are also mostly self-interpreting).
The two most obvious example of self-interpretation are
- when Abraham describes an abyss which the rich man should have been able to see,
- when Abraham ends the story by warning that stories of the afterlife won't be effective in making people repent.
That last is especially convincing to me: if that had been a real story giving real details, then there is no reason to end it with the warning that giving real details won't help.