Generic term for 'one who is being told a story'

Since you want a more 'medium-neutral' term for this, consider these options:

story-receiver

story-recipient

story-experiencer

.

narrative-receiver

narrative-recipient

narrative-experiencer

"The focus of narrative analyses has been on the story and the teller. More attention needs to be paid to the role of the story receiver in creating narrative meaning"

"We can study narrative from the vantage point of the storyteller or the story receiver..." "The storyteller chooses what story information to present and to omit. The story receiver pieces together the information presented as well as hinted at and creates the story in her or his imagination."

"...on the part of both participants (story-teller and audience) that indeed a story is being told, that there is present in one place a story-teller and a story-receiver"

"At these moments, one can hardly distinguish between the story giver and the story receiver, for it's in the shared experience that the dragon appears."

"The concept of point of view involves the relationship of the narrator to his story and to the story's receiver."

The circuit of communication is now completed: narrator, story, receiver, response. The "story", however, need not have plot or action.

"The opposite of a storyteller, she was a story receiver."

"Narrative has the power to create such worlds, imagined communities, or mythical nations, which on certain occasions can supplant the “real” world in the mind of the story recipient."

"Most narrative researchers consider storytelling to be unlike everyday conversation in that the teller monologically performs narration, an audience exists as story recipient..."

"It is significant that Munro often changes between first- and third-person narration in successive versions of a story without changing our sense of the story's experiencer."

"3) locate and describe, narrate into existence, an audience as narrative receiver, and, by extension, give form to a conception of the world."

"The metaphor, whether cultural or private, was heard by the listener as an element of performance style — something that made the oral performance an emotionally satisfying experience for both storyteller and narrative recipient alike."

"For example, directly addressing the reader normally compels us to acknowledge our role as narrative recipient; but these addresses are minimal in the early chapters of Jane Eyre, though they increase dramatically near the end of the novel,..." ~ Charlotte Brontë and the Storyteller's Audience

"Finally, we must distinguish between the “incident narrative” (that of the “narrative experiencer”) and the “courtroom narrative” (that of the in-court legal storyteller). "

As far as I could find, we refer to the generic audience as a version of the verb used to receive the story suffixed with -er.

Watching the 5 o'clock news makes you a viewer. Reading a dental pamphlet or work of fiction makes you a reader. Listening to a story makes you a listener.

See Audience for examples — Dictionary.com (bolding mine)

noun 1. the group of spectators at a public event; listeners or viewers collectively, as in attendance at a theater or concert: The audience was respectful of the speaker's opinion.