I've been presenting this as an 'interactive story' because I think that definition suits it but there a lot of people who think because you press buttons/control a character on the computer that it must be a ‘game’. I was trying to push those boundaries and play with the assumptions that wider audiences themselves have constructed.
Hm. Have you explored other games that push/cross those boundaries yet? There are a lot of often obscure games that blur or completely erase the line between 'game' and 'story'. Judging from IRTR, I'm guessing you've at least played Every Day the Same Dream, but there are many other games that cannot be simply described as just 'games'. Especially the visual novel genre (and games inspired by it) often come closer to stories - while there are VN-like games that can without a doubt be described as games (things such as the
Phoenix Wright series,
Time Hollow and
999: Nine Hours, Nine Persons, Nine Doors), there are also games where gameplay is very limited and only an addition to the story (
Little Busters!,
Rewrite,
Digital: A Love Story,
every single visual novel with gameplay), "games" where the only user interaction other than clicking through the text is making choices (normal visual novels like
Clannad,
Ever17,
Fate/stay night and
Steins;Gate), and even "games" (?) which don't even have choices and just present a clearly linear story to the player (linear visual novels such as
Higurashi no Naku Koro ni and
Narcissu).
All of those titles take more inspiration from literature than from cinema, though, with narration mainly being text, text and more text rather than visual information (though there are exceptions - the recent
Mahoutsukai no Yoru, for example, has mind-blowing animation for a visual novel, and
School Days is fully animated like an anime series). It would be interesting to see more from the cinematic side of things.
From the less story-focused side of things there are also many games more aimed at delivering an interesting experience than presenting actual gameplay. Popular examples include
Yume Nikki (Dream Diary),
LSD and the games from
Tale of Tales (though I haven't tried those myself yet).
If you're already familiar with all of this, just ignore my post. If you aren't, try them out, they might be inspiring.