This might not be in common usage, but consider storygoer, formed on analogy with with theatergoer, moviegoer, filmgoer, and concertgoer. It means:
a person who entertains a story.
This word is used. For example, it is used in the following passage:
Stories always have a situation, however minimal, whether given through description, narration, dialogue, action, or otherwise. Beyond merely suspending disbelief in order to entertain a story, the storygoer who holds nothing back allows the imagined to gain an actual reality.
Soderquist, Kierkegaard on Dialogical Education (2016)
An alternative is storyhearer, which is generally used to mean anyone who entertains a story, spoken or written. This definition is evidenced by example occurrences here.
Another alternative is storyship, formed on analogy with readership and listenership. But storyship would refer to the collective audience, not a single person.