It's not difficult to make the decision and the path significant if you use variables for delayed consequences. If I walk through the house and that gives me +1 to my "Direct" stat and I walk around the house and that gives me +1 to my "Sneaky" stat, they may both led to the same place, but then I can accrue these small stat increases and turn them into real consequences later in the game. Then the astute reader can be happy.
I can certainly do that sort of thing Cave of Time style, but it would take *much* longer and I'm not convinced the results will be better enough to balance out the exponential workload in any game of great length.
The CoG answer to that is to have a button that you can always press to see stats. But you hardly need that. Some people like it, but I imagine others never look at it.
But whenever "stats" come up, people who care about stories always get worried because they hear "stat" and think "strength" or "constitution" and then think about the impact on game v. story. Me too! But "stat" is way more general than that, and can include really anything tracked, like, did you notice the poker player's three distinct tells (the "Tell_noticed" stat goes up) or were you a jerk to your parrot (the "animal_cruel" stat goes up) and so forth. And you wouldn't want or need to track that visibly for the reader.
The reader *knows* they are being a jerk to animals. So doing the delayed branching respects that by having a result later accounting for the stat (if animal_cruel >= 3, then blah). Cave of time can branch to do that, but that has the problem of being unable to deal well with slow accumulations of small changes that avalanche into big stuff, because it's so well-suited to big changes at every decision point. Both are cool.
I mean, my choose your own prompt contest entry was stat-reliant to make different outcomes. I don't think people were "stat focused" while reading it either... The key would be to have various branches still possible so that it wasn't just the "right" and "wrong" answer. My goal for that game was to make every outcome of the puzzles equally entertaining and long. Granted, you did die in some of the branches, but you lived in most. My game was also short; any of the complete branches could have continues though (unless you were dead).
Cave of time seems like the easiest and best type of game to write. Experimenting with crossing paths in a long game is difficult because the background information the character has either had to exactly match or not matter. Still, having variables is a nice flair, and they can be used in a long story to make something cool.
As for the "how do you alert readers of the stats" thing, making it obvious what choices affected where they are at seems like the way to go. Being too obvious could be a problem, but in the "walk through or around the house" example, you could have the main character find something in the house (no need to use items, they just find a flashlight or something) then later you either can see on the dark tunnel or can't. If you can't maybe adding a line like "maybe if I had looked on the house I would have found something to help!" To let the reader know where they went wrong. I don't have the most experience, but that sort of thing seems to work well...
You almost have to explain the looping for this to work, otherwise you character is inexplicably gaining meta knowledge from a story perspective. I agree that it can be really cool if done well, though.
Every time I write a time cave I have to consciously stop myself from writing too much lest I risk it getting out of hand and getting burnt out on it; usually I just cut a branch off when I feel it's getting too long, leading to the branches feeling neutered.
There are ways to do this without bottle necking. If a game has fixed plot points that happen in order independently from player choices, then you just have to write each event from a different point of view in each path. For example, when your theoretical kingdom is invaded maybe you can be in one of three spots:
1. In the kingdom, tasked with defending it.
2. In the kingdom, but using the commotion to escape from prison
3. You left awhile ago and defected to the other side, so now you are leading the attack with intimate knowledge of the kingdom
This type of story sprawls out of control and almost has to be long... My long fantasy WIP is based around 4 major plot events. Based on your previous choices you are in different locations and different things happen, but the same 4 events do happen. You can be good or evil, and fighting with or against almost any character. The result is something like 16 full length endings to accommodate all of the options. That is why the game is also looking to be around 150,000-200,000 words minimum.
Cave of Time is dope as heck, but I'm not quite used to writing it. Most of my stories seem to be a bit more linear and use the bottleneck and gauntlet method and such, with most side branches being the same way.
I have like, possibly one true Cave of Time style storygame planned for...some point in time.
Altho I think I will like writing large branches that reconnect later on eith smaller choices and quick branchings in between
Also to avoid the plague of writing similar things multiple times.
I'm still figuring out what sort of style I like best, but I think I gravitate towards branch and collapse (gauntlet?) stories that have the same or similar key scenes. Although my last story was literally a pilgrimage with a set destination, so sort of had to be. But even the one I did on Infinite Story had some scenes identical or near identical in different branches.
I'm working on a poetry one that is more Cave of Time (I think it might join up in a couple spots, but not many) - but I need to make a flowchart for it before I add any more, as it's already hard to keep track of.
What you are describing is (I believe) the style known as a "funnel." A gauntlet is a linear story where a "wrong" choice leads to a instant death/ending.
I reread the big article on branch types, it's branch and bottleneck. My Book of Vanishing Tales rejoined up at cities/ports and at the destination, though there were different routes one could take. Blade of the Hollow was far more branchy, but essentially collapsed down at a few key scenes back into 2-4 branches if I recall.
I can certainly confirm that writing a Cave of Time style story is more fun than a game-like story. Planning for every single combination of choices a reader could make is often tedious and sometimes I get into my own head, wondering about the implausibility of the number of people reading the story coming across a specific piece that I'm writing. Even if your game-like story has only a few variables, it can get pretty outrageous.
Whether or not it's more fun to read relies heavily on whether the person who wrote it took care to heed to game mechanics, rather than just the writing portion. Instead of just writing a cohesive series of storylines, you now have to start thinking about how to direct the reader to the fun. Game-like stories without this can easily be seen as dull, when perhaps you didn't play the game the author intended for it to be played.