Literature that is not simply read from start to end in the normal way.

This is a but vague, so examples may help. Choose your own adventure series, House of Leaves, ELIZA, One Hundred Thousand Billion Poems.

If you want to stretch the idea, you could consider LLM output to be ergodic literature of the training data in that it cuts up the corpus and resynthesizes it.

Strange term, choose your own adventure is non-ergodic, there are many failure states you can land on. Meanwhile, most normal literature is already ergodic under the normal definition.

I looked up the definition, and I'm still a bit confused. I'm familiar with word in the context of traversing system states, specifically graph traversal.

The term "ergodic literature" doesn't seem to relate to the word in a math context which seems strange. Usually the same word used in different domains has analogous definitions.