I was only trying to find an agreement on terms. I never typed "GNS" or "GDS" because that wasn't my point. It is difficult for me - I'm slow - to follow a discussion when I can tell those involved don't understand what they are talking about. By "understand" I mean different people posting in the discussion have different interpretations of key words being used.
No, I totally get that. But getting into those three categories like you started to there I think is a digression, not directly germane to what this particular discussion is about. Those are stances, attitudes, agendas.
Assume for a moment that my theory is correct- Reynard didn't mean "narrativist" as in an agenda of play or preferred STYLE of play, but simply "narrative" as in "story". Like Umbran suggested (below), but Reynard was talking about carrying it a step further.
I think a good broad description (if not definition) of a "narrative mechanic" is a mechanic in which someone at the table gets to choose how to more directly influence the narrative when they wouldn't otherwise do so.
I don't really think typical critical successes and failures in D&D are particularly good examples of narrative mechanics. For one thing they typically put that narrative control on the GM, who would typically be the one narrating the result of a d20 roll anyway. For another, for much of D&D's history, folks have been ensconcing the results of critical success and failures to tables or simple rules, such that the GM isn't actually choosing the result.
So as I understand it, Reynard wasn't asking about narrativism vs. gamism vs. simulationism. We're just talking about whether D&D players, playing D&D (in whatever style), take 1s and 20s as opportunities to change the story more than they would otherwise if they followed the book and were just treating them as simple failures or successes.
This is a practice we see referenced in memes and jokes all the time (or at least I have, for some years, YMMV). But as he pointed out in the OP, this seems a bit at odds with regular or by the book D&D play, which ascribes all narrative responsibility to the DM, and doesn't account for "extraordinary" successes or failures except for critical hits in combat.
So then we get the three initial questions:
What do you think? Are 1s and 20s unofficial "narrative mechanics" in D&D (especially 5e)? Do you give those results extra weight (beyond critical hits in combat)? How does it square with how you perceive games with explicit "narrative mechanics"?
My answers:
1. I think they can be, and seem to be at some tables.
2. Sometimes, especially in a more casual game and with newer gamers. I think with a table of hardcore experienced players and an ongoing campaign I feel less need to add extra color or a plot twist on a random skill check, and I am less likely to want one to potentially derail things that often. But in a casual game and with newbs it adds to the "gambling" excitement, and having more twists or "pop" moments to riff off of can make it more fun.
3. I think the randomness of when it comes up makes it less offensive to players who are uncomfortable with metacurrency. They don't feel the same degree of removal from immersion that they do when players have, say, "hero points" or "whimsy cards" or something they can choose to spend at any time, which inherently puts part of their mind more in author stance than in actor stance. If I have a whimsy card I can spend at any time, I'm probably inhabiting author stance at least partially at all times, if I want to keep an eye out for when to use it. Whereas if I just get a moment of narrative control when I happen to roll a 1 or 20, then I can spend the rest of the session focusing on inhabiting the character and only "pop out" of that perspective when the dice tell me to.