why Eliezer has described his own work as "fictional literature from what looks like an entirely different literary tradition."

Characters in HPMOR do things for rational reasons. Smart characters are smart and make their decisions based on careful thought instead of unexplained flashes of insight.

That not something that happens in normal fiction. If you think that's not new, which works of fiction do you consider to have the same quality?

why some people are induced to change their life by it (perhaps only because it piques their interest for other material on LessWrong)

Because HPMOR often has morals to teach.

There are a lot of atheists who are essentially like Harry's father. They wouldn't run experiments to test whether magic exist but simply assume that it doesn't exist and get angry with everyone who claims magic exists. By having a well written story they might update into the direction of empricism.

It teaches a version of science that about experiements and not about reading authoritative papers. That might raise in at least a few readers the question of why they aren't doing science in their lifes.

The narrative about taking heroic responsiblity is strong. For me it was strong enough to make some decisions about taking responsibility that I otherwise might not have made.

To me HPMOR feels deeper than Pratchett. Pratchett makes a lot of points on the surface and plays around with them. HPMOR had a bunch of instances where Eliezer made point that weren't obvious and buried deeper. Enough for most readers to not consciously get them, but that doesn't prevent the reader from absorbing the moral a more unconscious level.

In hypnosis telling metaphars that take the brain months to understand is a teaching device for creative deep belief changes. HPMoR frequenlty makes point on that level.
I would not have expected to find that in writing by someone like Eliezer and it made me update into thinking that Eliezer understands more than I previously thought. Eliezer doesn't have a hypnosis background but learned his lessons about deep metaphor somewhere else. Probably by dealing with zen koan's and how they are used for teaching.