Travel times and distances don't matter in this game. In John Boorman's Excalibur, how far did the knights ride on the Grail Quest? It doesn't matter. How long did it take Arthur to ride from Camelot to his final confrontation with Mordred? It doesn't matter.
In a novel with only one moving piece, it doesn't matter. In an RPG where one assumes at least a passing nod to realism is being given (and if it isn't, I'm out) if the main party goes north for three days (say, 45 miles made good) and the PC with the villagers goes south for two days (20 miles, they're moving slowly) before finding a refuge for them, if the PC with the villagers now wants to leave them and catch up to the main party how long is that gonna take? 65 miles...assuming normal movement rates etc. that's 3 quite long days or more likely 4 reasonable ones; and that's assuming the main party stays put and doesn't go further north.
Going back to the Middle Earth example - this would have been something JRRT paid meticulous attention to, with all the different pieces in motion across the setting: time and distance.
As best I recall, everything that is learned about the history of the Ring comes out either through Gandalf telling Frodo, or through various speakers at the Council of Elrond. Unlike the film version, there is no abstracted narrator who tells us this stuff.
But notice that we never learn (for instance) the history of the mayors of the Shire, nor the history of the rulers of the Southrons, nor the nature of agriculture near Laketown and Dale, nor exactly how hobbits get their cheese. There is an indefinite amount of stuff about the world which is not part of the story.
And passing mention is made of a surprising amount of it in JRRT's books, leaving the reader often wondering "what's the story behind that?". This is why his estate has been able to keep churning out supplemental books, is to answer these questions.
And in game play, all the stuff that anyone cares about can come out in play, by focusing on the actual concerns of play. Mechanics that can produce it of course vary from system to system, but plenty of systems have mechanics of the right sort: whether those are Lore mechanics, or contacts mechanics, or mechanics for influencing NPCs, or perception/search mechanics, or whatever.
I say it's still good to have those passing mentions in there, if only to fuel curiosity either then or later.
Here is an actual play post
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I don't think that is lacking in depth or colour. But it did not depend upon the GM introducing random details of intersections and beaten slaves.
That looks like some cool stuff there.
However, it's perhaps a tangential example to what I'm saying, for these reasons:
1. In your write-up it seems the various locations referenced are quite close together - each a staircase apart, if I read it right - and so there's very limited opportunity (or need) to introduce intersections and-or other geographical features.
2. This seems to be an example of epic-level play (one of the PCs is already a god, for Pete's sake!) near or at the end of a campaign, which implies most of the fundamental choices have already been made and any earlier distractions long since dealt with. It's a bit late to be introducing something as trivial as a slave being beaten.

Yet with that said, you were still introducing DM-driven complications...
3. Further to 2 above, we don't see here how direct or indirect the party's path has been to get to this point; how often they veered off course, or whether there was any point when they could have lost the trail of the story entirely and thus never got this far at all.
You are assuming that, in RPGing, this sort of dynamism can only be the result of GM-driven play. But there is simply no evidence that that is the case!
The PCs in my Cortex+ Heroic game set off to find out why the Northern Lights were behaving strangely, but have not yet got very far north. They arrived at a dungeon and entered it, but learned nothing of relevance to their mission. Instead, after getting teleported to the depths by a Crypt Thing, they ended up in dark elf caverns and one of them tricked the drow out of their gold while the others had to fight their way out and trudge home. Since then, they have been caught up trying to save the villagers whose village was destroyed by Ragnarok cultists that the PCs could not defeat.
Your analysis and assumptions completely ignores the significance of player choice (eg a player chooses to go for the gold rather than continue with the quest) and of failed action resolution (the PCs fail to save the village, and so now - if they want to rescue the captured villagers - have to postpone their quest).
Quite to the contrary, I'm not ignoring the significance of player choice at all - I'm advocating that they get the opportunity to make those choices in the first place!

They see a slave being beaten - do they divert to help the slave or not? They pass numerous intersections while traversing a passage with the angels - do they divert to explore these or not? While sneaking through the castle halls to a place where they can eavesdrop on the king's council they pass an open door to a bedroom full of treasure - do they (or does the party thief) divert to steal some or not? We'll never know if you-as-DM don't mention these little vignettes in passing and give them the opportunity.
This is what I'm after, and it has to come from the DM.
This is all assuming a GM-driven game. It shows a complete failure to grasp how player-driven RPGing actually works.
You may have read
these blogs, but I don't think you actually processed what they are saying:
The actual procedure of play is very simple: once the players have established concrete characters, situations and backstory in whatever manner a given game ascribes, the GM starts framing scenes for the player characters. Each scene is an interesting situation in relation to the premise of the setting or the character (or wherever the premise comes from, depends on the game). The GM describes a situation that provokes choices on the part of the character. The player is ready for this, as he knows his character and the character’s needs, so he makes choices on the part of the character. This in turn leads to consequences as determined by the game’s rules. Story is an outcome of the process as choices lead to consequences which lead to further choices, until all outstanding issues have been resolved and the story naturally reaches an end.
There cannot be any "the story" during Narrativist play, because to have such a thing (fixed plot or pre-agreed theme) is to remove the whole point: the creative moments of addressing the issue(s).
Frame situations that will provoke choices (and not just requests for more setting download), let the players make choices, establish consequences (which may be what the players want, if checks succeed; or not what they want, if checks fail), and then frame something new in light of that. It's pretty simple. And it will produce a story that no one new in advance was going to come. Without the GM having to provide a menu of setting elements for the players to choose from.
That sort of game really seems to assume the players will be quite goal-oriented; and if so I'd rather see the DM framing scenes and introducing vignettes in passing that are intended to try and divert them from their goals or frustrate them from achieving such, rather than just relying on the luck of the dice to provide you with these opportunities.
And if a group of players aren't necessarily that goal-oriented and just want to play for gits and shiggles, how's that gonna work?
Lanefan