what is the term for a work that makes the reader part of the narrative

[tantric]

House of Leaves in print and the Ring in film being exemplars

[Red Terror]

House of Leaves in print and the Ring in film being exemplars

In Postmodernism literature it is called Audience surrogate.

https://en.wikipedia.org/wiki/List_of_narrative_techniques

A parallel story follows Nicholas Branch, a CIA archivist of more recent times assigned the monumental task of piecing together the disparate fragments of Kennedy's death. Branch concludes that the effort will be never-ending and the whole truth ultimately unknowable. Branch is an example of the reader appearing in the novel itself, one of the postmodern phenomena that marks DeLillo's work.

https://en.wikipedia.org/wiki/Libra_(novel)

[Danik 2016]

Thanks for the useful link, RT.