Ok, I am not familiar with narrative game mechanics, (My players are not interested) but my understanding is, that in narrative games: There is a formal process where a player (not the DM) can propose a narrative and the DM, perhaps others) can accept or contest that narrative and if they contest the narrative then mechanical resolution decides whether the proposed narrative is accepted entirely or with modification in to the fiction of the game.
Plot points seems pretty brutal and do not have a dispute resolution mechanic.
A secret door appears where none previously existed or a hidden diary that reveals the bad guys plot suddenly.
Are there other approaches to this, and what would they look like.
I don't think "narrative game" is a term of art.
"Narrativism" is a term of art in a certain RPGing subculture, namely, The Forge and those who still use their jargon. In that sense, it is glossed as "story now" and is contrasted with "story before" (eg most post-DL modules for D&D, which have a built-in plot) and "story after" (the OSR-ish idea that there is no story to play until after the event, when you tell war stories).
"Story now" RPGing needs systems and processes that allow meaningful (in a literary or artistic sense) questions/conflicts to be posed and answered through play. Eg in a 4e D&D game this might be
Is a Dusk War inevitable, or can it be averted? In systems like Burning Wheel or Apocalypse World, normally the concerns of play might be more personal or intimate, like
Can Thurgon liberate his family estate from its degradation while staying true to the ideals of his order?
The more that resolution is dependent on the GM making stuff up, the harder it is to get "story now" play - because really we're just finding out what the GM thinks. The GM isn't him-/herself "discovering" the story just as the players are.
Player-side stipulations (which sounds like what D&D 5e plot points are, judging from your post) are not particularly relevant to "story now" play either. OGL Conan has them (called Fate Points) but is a system that aims pretty much at traditional GM-storytelling play as far as I can tell. Burning Wheel doesn't have them, but is one of the better-known "story now" systems.
One thing that is fairly distinctive about Burning Wheel is that it deals with many of the same tropes as classic FRPGing, but it uses different techniques. In D&D, as traditionally played, the action declaration
I attack the Orc is resolved as a check - and if successful, the upshot may well be that the shared fiction includes a dead Orc; but the action declaration
I search for a secret door is first filtered through a GM decision as to whether or not a secret door is present in the location being searched. Only after the GM answers "yes" at that filtering stage might a check then be called for. BW treats both action declarations the same: if the check to find the secret door succeeds, the PC finds a secret door as desired; if it fails, then some adverse consequence (that follows from the established fiction) ensues.
The same process applies to the declaration
Having returned to my ancestral estate, I hope to meet my brother.
These mechanics don't magically give you "story now" RPGing. But they help support it, because they allow players a much greater degree of capacity to contribute to the shared fiction, and thereby to drive the direction of play. If these sorts of checks succeed, things move in the direction the players hoped for their PCs. If they fail, then adverse things happen which follow from the established fiction, including the declared check, and hence have immediate thematic relevance. So the vagaries of dice rolls means we get an ebb-and-flow of success and failure, but all thematically related to the PCs' (and players') aspirations. Ie we get story
now, in play, without anyone having to author it.
There are "story now" oriented RPGs that don't include these sorts of mechanics (eg Prince Valiant) but they use other devices to ensure thematic relevance and avoid having the direction of play depend upon GM exegesis of pre-authored fiction.