And on that note, PbtA and Forged in the Dark games also have a strong Narrative element to them, despite being different from older definitions.
That I would agree with. There are a lot of modern games that are "informed' by the Forge discussion and a lot of the conversation that it spawned without meeting any sort of pure agenda definition that Forge would have recognized.
One problem that causes though is you have a lot of people looking at these disparate games and categorizing them by "do I like them".
I have a good deal of respect for what both PbtA and FitD are doing and they've both been tremendously successful and influential.
That said, a lot of the claims made about them are not defensible, but just part of the long running pattern going back to the 1980s of people going, "My choice of games proves I'm a better gamer than you." Back in the 1980s it was often "My game is more realistic and makes more sense than your game." Now it's usually, "My game is more narrative than you", which is the old 1980's "role player does not roll player" pretension.
On the topic, "Daggerheart" is clearly informed by modern gaming theory like "fail forward", a single generic resolution mechanic, and the inclusion of meta currency. But it's also clearly informed by classic gaming with things like granular weapon and armor lists. To a large extent, the classification of it into "nar" or "not nar" feels to me pointless. It's an abstraction people are using to discuss it based on whether they like or don't like those things. You can make arguments either way because the designer isn't trying to be pure about it, and really people are just defending that they like or dislike the system (or some other system). For me I see good points in the rolls as a group system and the fact that it does always give the GM an out for its "consequences" roll of just taking metacurrency if it's not obvious what the consequences should be.
For my part I don't like or dislike "nar" or "not nar". They each have their place depending on what you are trying to accomplish. Which is better a socket wrench or calipers? I do greatly dislike the very broad claims about what is possible for a gaming system and the lack of exactness - confusing "player driven" with "character driven" or claiming that non-nar games aren't about stories or don't have PC protagonist or claiming that nar is such a vague concept that you can do it with any game system and such is just... poorly considered.
But as for "Daggerheart" I dislike mostly the barely controlled chaos of the system and the fact that if you had different levels of extraversion in the players in the group I feel like the introverts would be pushed to the back harder than normal. The lack of taking turns gives me as a GM a lot of pauses, because you now have almost nothing to force characters to share the stage. I see why because turn based creates oddities, but I'd put up with the oddities over chaos and people arguing over who should take the next action. I also wonder what the extra granularity of "with hope" or "with fear" would actually do for me as a GM besides make running the game a bit more complicated. I don't think it's the right game for my players, and I'm not excited to run it because I don't see it giving me any stories I can't already tell or any scenes I can't already generate with other systems. As a potential player, it doesn't feel particularly empowering to me because disassociated mechanics and the fiat addition of stakes always favor the GM. I always feel these sorts of mechanics are there to make railroading easier. But you know, I wouldn't not play it either if I have the right GM with a flair for story telling. Whether it's "nar" or "not nar" doesn't really enter into this.