"If you want to be nitpicky", you can insist that the overall process is not an exploit because it does not directly rely on FFXIV's programming to work.
I would debate that part of it - it seems to rely on the nature of how the game handles cutscene playback - but even if it is "only" a Windows exploit and not a FFXIV exploit, it is still using an exploit of one kind or another to get around the forced cutscenes.
The clear design intent (in the current build of the dungeon) is that everyone is locked in place until a cutscene ends, and progresses through the dungeon together. (We know that is their intent because they have said so - that the change has been implemented to ensure that new players can experience the dungeon as intended, without being rushed or left behind.)
The flaw is that they can't directly lock players in place for this, and instead implement it by locking them into the "viewing cutscene" status. When the game is running normally, there is no way around this status.
A second flaw is that the game does not (and possibly cannot) reapply the "viewing cutscene" status to a player logging back in after a disconnect.
The vulnerability which they cannot program against because (as you said) it is above and beyond their software, is that people can do something they would not do in the course of normal gameplay: deliberately force-quit the game and then log straight back into it.
Put these things together, and you can deliberately quit and log back in to be free to move when the game intended for you to be still locked in the cutscene.
That is an exploit. It takes advantage of how the different elements of the system interact, to do something outside of what the programmers intended.
This is guesswork, but I think it's programmed differently between single-player content and multiplayer content.
In single-player content, it works as you described. A cutscene is triggered by interacting with an NPC or objective, and is only marked off as 'done' when you (the only person involved) have reached the end of it, or opted to skip it.
In multiplayer content, I think it has to work differently to accomodate the fact that there are four/eight people having the same experience together, and possibly the nature of the instanced content.
As I see it:
1. A cutscene is triggered when one party member reaches a flagged point. Everyone watches the cutscene simultaneously.
2. At this point I believe the flag is removed and/or the cutscene is considered 'played', preventing it from playing again when the next person reaches the flagged location.
3. Disconnecting and returning to the instance does not reset the flag. The cutscene has been played, it's done, and it will not trigger again during this instance.
As much as they want everyone to be able to watch the cutscenes, it's probably necessary to handle "unintended disconnects" this way - even more so after implementing the forced scenes. Imagine if someone with genuine connection issues kept getting thrown out of the game, logging back in, and having to watch the same cutscene three-quarters of the way through before their connection broke again? They'd be stuck there for ages.
Also worth mentioning, I had the misfortune to start my original run of Praetorium just as the system came under a DDoS attack. It was disconnection hell, and a curious side effect of this? If I was disconnected when a cutscene was triggered, not only did I miss seeing it, but the system didn't even recognise that I had unlocked it. The Unending Journey cutscene viewer only contained the scenes I'd been present for, and a second run through the dungeon doubled the number of cutscenes listed for it.
Without actually checking the ToS, I would expect it says you cannot exploit flaws in the game programming to gain an advantage, or affect another player's experience.
Argue the semantics all you like, but I am fairly sure this is exploiting a flaw in the game programming - specifically in the method used to lock player movement and prevent some from moving ahead of the group - that is only exposed in conjunction with a Windows function that the programmers cannot prevent you from using.
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I should add that I found a game exploit myself, once. Just a mobile game that unlocked more characters and items according to your running total of high scores. It happened completely by accident - one time I was having trouble submitting my score to the leaderboard, it kept getting knocked back, and I eventually realised that my internet had dropped out.
When I turned it back on and submitted my score, I got credited for every attempted submission of that score. Hundreds of points and gems and whatever it was the game ran on. So I did it again deliberately a few times. I got all the characters and skills unlocked in a couple of days instead of weeks or months of play.
In this case, it affected nobody except myself (and the company throwing out cheap mobile games intended to suck you into paying for extra credits). But it was definitely an exploit. The fact that I found it by accident doesn't change that.