I think almost all of these are innovative in some respect, and there are loads of other things that are also innovative in other respects – 80 Days for its combination of board game mechanic and story, 18 Cadence for letting you construct your own poetic interpretation of fictional elements, etc. Even things that are straight-up gamebook adaptations or re-inventions (inkle’s Sorcery!, stuff from Cubus and Tin Man Games and Choice of Games) often push in some interesting way on the game-story interface.
But it sounds like possibly you’re specifically for something that is a) as consciously literary as possible while still using sound and graphics, b) not necessarily a game, and c) specifically playing with the expectations of linear narrative, reader relationship to the text, and perhaps layers of fiction and frame story/annotation? Is that about right?
I’m not sure any of these is quite on target, and they’re not apps, but collectively they might interest you:
daddylabyrinth (Stephen Wingate) is a biographical/autobiographical website about the author’s relationship to his father (my review here). If what you’re looking for is the sensation of constructing meaning by doing research-like activity through a large body of material (and maybe getting lost, and maybe not being sure when you should consider yourself “done”), daddylabyrinth pulls that off.
Patchwork Girl is a classic (1990s) piece of hypertext literature that requires assembling meaning from fragments. It used to be unavailable for some computers, but it looks like Eastgate Systems is now able to distribute it again.
Solarium (Alan DeNiro) is a supernatural cold war narrative with light graphics and some beautiful writing; it employs loops through the text to good effect, so you wind up revisiting certain passages and finding that they have new meaning when you get there. My review is here.
Living Will (Mark Marino) is a document that purports to be an interactive will, in which the terms of the will depend on how the heirs respond to the document. Light multimedia with some maps. My review.
Colorado Red (Alice Maz) is a piece about same-sex lovers during a mining strike, with some embedded pictures. Some of the text has annotation links; when you hover, you bring up the protagonist’s thoughts about what is going on, which are otherwise obscured.
Pale Blue Light (Kazuki Mishima) puts the reader into the story at different layers of fiction – at some points you’re interacting with or as an author, and sometimes on the level of the characters in the author’s story. This one is parser-based and maybe more of a challenge to play than the others listed here.
And with the usual disclaimers about mentioning one’s own work: First Draft of the Revolution is an interactive epistolary story, by me with tech by Liza Daly and inkle; the conceit is that you’re actually altering letters before they’re sent.