I am ecstatic about these games. I still don't feel there are enough of them out there, and those that are get what I feel is a disproportionate amount of negative criticism, which I consider reasonably indicative of a widely-shared negative bias. So, up front, you'll need to deal with "this game is not a game" views if you're looking to interest as much of an audience as possible. But the biggest thing is that you will need the skills to pull off writing, camerawork, pacing, and so on, where there wasn't as much of a necessity before. Without a strong gameplay for people to default to with "the story sucked, but it was okay for a game and the gameplay was fun", things like the plot, exposition, and even "director"/"showrunner" polish behind the audiovisual presentation will be shoved in the spotlight and impact the resulting experience much more, catching more flak as a result.
Don't underestimate the time or breadth and depth of experience any of those have to accomplish. If you want to truly nail what a "movie-game" is in essence, you might consider having additional teammembers (e.g. scriptwriter for plot and characters, designer for "director" elements and details behind camera movement or character behavior/dialog, musician/sound technician for creating and mixing music and sound effects, artist/designer for any or all of: character/set concepts, any lighting in your game, animation, and such) to handle/review any weak areas you might have. Their expertise might ultimately prove more invaluable than your own visceral proximity in producing as much as you can.
As a last note, "minimal action" doesn't mean no action. Presumably things will happen in cutscenes anyways, but it seems ideal in your position to try to find a clever way to create player interactivity. Most of the games under your descriptions mistakenly brush it off with the infamously default QTEs (Quick-Time Events). While QTEs are acceptable by themselves, it probably shouldn't be the predominant force behind your video game that keeps the average videogamer alert and ready to do stuff, and same goes with other rote actions like memorizing passcodes or solving tedious puzzle gates. Some slick and relevant way to keep the player engaged (mentally and/or physically) both in the action of the game and in the story is important. And here the gameplay can stay relatively constant through the game and even take advantage of character-player progression with upgrades or fluctuate drastically to mix things up simultaneously with the plot/character, or somewhere in-between. This is just in reference to the brief description of your game idea; you may already have this figured out.
But another consideration to keep in mind is that having the gameplay consistent with the story and character can make your movie-game more effective as such. As an example, a popular draw for people: not having an experienced character mourn over their first encounter in taking another being's life to elicit audience empathy and then proceed to force them to kill hundreds more without appropriate framing (or, otherwise sacrificing gameplay parity with story or holding down the story with obligatory gameplay). In terms of "professional" production, keeping cutscenes frequent and short as well as fluent with the visual/aural game is vital for maintaining pace in these sorts of games. So, that would encourage real-time cutscenes that don't behave too differently from the rest of the game, avoiding things like having characters only speak up when a cutscene is prompted or having both deliberate and unaccounted inexplicable jumps/inconsistencies in chronology, character design, or whatnot.
If, after reading this and upon further deliberation, this seems out of your scope in terms of capacity or aspiration, remember that you don't need to make a "movie-game" in the way you have described to make a cinematic game. There have been plenty of great games that force constant player interaction (i.e. gameplay) but ostensibly put their story in the spotlight. But when looking closely, or given some time, the sheen begins to wear a bit and more people may being to criticize both its story and gameplay for lacking in depth. One of the most recently appraised of which may be The Last of Us, which created a beautiful world with fantastic production quality and solid gameplay. But, stripping its story and gameplay down, it's not all too dissimilar from other games with a straightforward story and relatively basic gameplay that maybe just didn't have as much in the way of polish or production (oversimplified a tad for the sake of argument). Other games like Thomas Was Alone managed to tell a pretty touching story that all-in-all could be written in a few pages, but was framed very well using narration, music, art design (namely color; minimalism), and even the gameplay itself (wherein gameplay imbues meaning to the story and the story gives meaning to the gameplay, symbiotically). There are a lot of other games to be brought up here, not least of which would include Quantic Dream's works that offer a lot to learn from and avoid, but what I mean by all this is that you shouldn't get stuck in the rut where "movie-game" means "a movie with a lot of game stuff to it" or "a game with a whole lot of movie stuff in it" when you can look at it as adding another sense to the audiovisual senses of a movie or another sense to a game. You can think of it as a shift from a silent movie to a modern movie--adding the sense of sound, the lack of which doesn't necessarily detract from the plot's content, but can add quite a bit to the experience of it. However much you agree with that analogy, it's valuable to still treat your gameplay or story--whichever you purportedly emphasize less, but may still put equal effort into--carefully going forwards.
I hope this helped a bit, if any of this was new to you or helped generate some thoughts, since I wanted to share my view on this broad categorization of games anyways. I really do want to see more well-made "movie-games" around, so I hope you follow through with this idea. It goes without saying that, about my suggestion to take on a team (film crew!), the extent of the game/movie can be scaled up or down as appropriate or even to fit your focus or your "budget", whatever it is made up of in time or money. Good luck!