For me, this goes back to the matter of terminology, and what it is being used to convey.
"Story now" was coined to describe a certain sort of game, where the core logic of play is for the GM to establish situations that permit the players to
say something. This means the situations have to involve or present "premise" (in the literary sense) and the players' choices respond to that premise and produce "theme" (again in the literary sense).
Because of the form of RPGing, in which the players' choices are manifested primarily by way of declaring actions for their PCs, it's essential for this to work that there be quite deep connections between situations and characters. Given that another typical aspect of RPGing is that
players build their characters, establishing that deep connection means that the players, as part of their PC build, establish elements that the GM can draw on for situation:
relationships,
kickers,
PC goals/aspirations/beliefs, etc.
Now maybe many RPGs produce story in the sense of not just a transcript, but a transcript with
"a 'little something' . . . a theme: a judgmental point, perceivable as a certain charge they generate for the listener or reader". Personally I've got doubts - I think a lot of typical RPGing does not generate story in the sense. But even if it does, it doesn't generate it in the way described in the previous paragraph - by having the players
say something in virtue of the actions they declare for their PCs, which are able to say something because of the situation the GM has framed.
A very obvious example is where the GM is running an AP, which establishes the villain as part of its contents - functionally, therefore, as part of the GM's prep - so that the players have no choice, in play, but to confront that villain via their PCs. In this case, even if the confrontation of the villain by the PCs generates a theme-laden story, it is not doing so as a result of the players' choices. The choice was made by the author of the AP.
In the play of this AP, we might say that in play we find out what happens when the PCs confront the villain (eg do they suffer defeat?). But we are not
playing to find out in the sense that phrase is used in Apocalypse World - we already know that the villain is the villain, and that the PCs will oppose them.
The preceding sets out some differences between "trad" play (I still put forward DL and Dead Gods as paradigms) and "story now" play. I'm sure a similar bundle of contrasts could be drawn for "story now" and "neotrad", beginning with the timing of when the player makes the choices that will reveal the truth about their character, ie as part of prep or part of play.
These very real differences in RPG play do not go away by insisting that all game play, or all RPG play, produces narrative. As I've posted upthread, all that insistence achieves is requiring the development of new terminology to describe these differences.