I think that with the type of game it depends.
Like a book or a movie never changes, even if you do. This often can have the eerie effect of never seeing the same story twice despite watching the exact same thing three different times in your life. But with a video game not only is it possible for that to happen, but to literally see a completely different story with different content each time.
I would say that what actually makes it such a problem is because vidya is a completely new medium in a for profit industry that doesn't have literally thousands of years worth of storytelling in its medium to fall back on, and in that regard one could easily make the same argument for books as one could for oral traditions, which are way older.
So in short, one of the biggest problems with vidya is also attracting pretty shitty writers and having lower standards for the audience with only a few decades of history to draw from in refining the medium.
In terms of what specifically you just described with filling in the blanks I would say this is one area where it can shine, and is probably part of why I mostly like city builders, 4x, crpgs and the like. None of these games had a linear story with the same predictable outcome no matter what which makes each experience often fairly unique.
The reason this is so important of course is also that I personally believe vidya has the highest potential out of any artform for the way the picture changes with you. There is quite simply no other medium on the planet that does that, which is why I think it can be a transformative, even borderline holy, experience that is simply underjtilized. Literally every single game session has the potential for being an elaborate psychodrama in a way that no other medium can possibly hope to match. I mean just think about it: Oscar Wilde envisioned such a thing in The Portrait of Dorian Grey
, a book written about a painting that transformed with the viewer as a reflection of his own soul. That is not something that could ever truly be tried before on one part of canvas and for once in human history you can literally watch it transform with you and showing you unique things each time.
Like take a 4x game for example. Your first biggest obvious choice is which race, and with one door opened the others are now all closed to what you will experience, and often what the subject says about your, your interpretation of them, and what you want to play. The other big choice is galaxy size, shape, how much water and so on, which also dramatically changes the narrative as everyone sharing one big map on islands is going to be more peaceful and trade based whereas all sharing a single continent or island is going to be a much more bloody one.
You make all these choices and then depending on game can try out different tactics and strategies and meanwhile nothing is really on rails, so you can deliberately keep a game going past easy conquest win to try and get a soft power win and see what happens and all along you're sort of telling yourself an epic space opera.
4x is well known for enabling this story to happen, called a recap story I think it's called. It also helps capture an often key ingredient of art, which is not pure possibility, but rather constraint, and it is often that constraint where the artist expresses himself more purely. In the form of a 4x, this becomes the actions of AI and random events with how the viewer reacts to them. It may seem as pure possibility, but it often forces your hand. And so, I think it enables a very good form of storytelling just there alone, although needless to say it depends on whether you mean it as for bydlo, in which case the written language becomes terrible romance novels, or whether it is the sort of person who considers everything as an artistic act.
I think the other key consideration is seemlessness of the artistry of one constructing it for you, which in DnD terms would more be the game master, much like the writer, who guides you on in such a way that your guided choices all feel as more spontaneous acts rather than coached decisions, which in a sense is what every artist is aiming for more or less.
In summation I would say that vidya has the greatest potential of any art form ever devised that is just often poorly utilized. I have encountered untold number of purely trash games for empty mindless repetitive entertainment, and yet there remain a few gems that have stuck with me for the longest time as a sort of collaborative storytelling. Among these are Planescape, Tides of Numenera, VTMB, and KOTOR 1 and 2, as well as to lesser degree Fallout and Wasteland 2. Personally I found KOTOR to be a nearly religious experience, though it may have also been time and place, and just purely on accident.
For instance, going in blind I had no idea just sticking my lightsaber in a vent was going to kill a guy. I kept thinking myself this big damn hero and justified my own actions and grey morality through that, long before realizing the epic plot twist, which became more absurdly blurring of the fourth wall as I not only accidentally killed the guy and thus both me and my character experienced going down that slippery slope to the dark side with the whole "I...I didn't mean to...I just wanted to scare him a little not kill him..." but also I kept trying to answer the computer at first with what I think
is the right decision or the "morally correct" choice to make and it failed me, and then I began answering the questions as i myself would and really bizarrely to me at the time managed to win perfectly once I realized I could pick the options for what I would choose personally instead of the ones I think are expected of a moral character. What I found was so fantastic partly because I didn't know that I really was Revan both in the game and by perhaps making one too many incredibly ruthless amoral decisions when fighting a war, which even offended one of my friends during a RISK game once because I needed to get my armies through his territory to face off a mutual threat and butchered in cold blood however many of his men on that territory and told him that army was "expendable" and to just take it back next turn
. I think it taught a greater lesson on war too, as I can safely sit here as an armchair twat and bitch about the British perfidy but quite frankly if I was in that position where the outcome of WWII was unknown it's entirely conceivable I would have sunk the French fleet and slaughtered my ally's sailors too just like they did.
This is quite simply not the kind of thing that can happen in a book. I can react to characters and the novelist can encourage me in a direction all he wants, but it's still the same story being told to me and thus can be rejected in a sense that vidya cannot. That so much of vidya is prosaic, formulaic bullshit is not the problem of the medium, in a similar manner to how scifi used to be thought of as the biggest piece of trash genre of writing out there whereas today it is pretty commonly accepted as one of the deeper thinking man's genres of writing.
I personally think that, without too many revolutionary changes in technology or societal collapse or whatever, that in a hundred years time vidya could easily be developed into one of the highest art forms in existence.
It also is sometimes completely unintentional. Like for example reviews of Star Citizen, or in my case some indie game where it was just my character trapped in a box in a dark room. It was by far a better avante garde experience than any insipid little art show I've ever been to. I saw an art museum in NYC and I was not impressed, although the glass garden was cool looking at least, but all of it was simply uninspired. But this? Being trapped in Unity engine in a dark room with no light, in a box, playing at night trying to figure out if I could even do anything at all? That was the first time I had truly been impressed by a piece of art in as long as I can remember.