Dungeons and Dragons

The campaigns my players consistently voice as their favorites are ones where I created an overarching plot, and then incorporated their backstories as significant and impactful portions of that plot. Being the sole input for character motivations for a story (as with a book) makes it easier to end up with a coherent vision and story, but more difficult because of the amount of content you're responsible for. Conversely a good DM can offload work to players and end up with a result that everyone is personally invested in.

I will say though that some DMs end up writing thousands of pages over the course of years spent in an ongoing campaign and might cry at your characterization.

It's definitely POSSIBLE to run a campaign without ever writing a page, but good luck when your characters get attached to an NPC you forgot about if improvisation isn't your forte.

DM's own the factory full of monkeys with typewriters trying to write their version of Hamlet

The players are the monkeys with the typewriters

It's not just you, but it's also not most DMs. TTRPGs are collaborative storytelling. Books are single-author and have a consistent plot (generally, anyway).

Some of us write books too :)

Yeah, pretty much. Collaborative storytelling is the most apt description I've heard. Could probably add "rng aided" and you've captured pretty much everything about it. It's definitely one of those "all about the journey, not the destination" sort of things, sort of like a road trip. Also like a road trip, can be anywhere from meticulously planned to basically being railroaded on down to "uh, how about that way?" or anything in between.

A nicer way of framing it: Co-creation is the heart and soul of tabletop RPGs.