CW: bullying, loneliness, powerlessness, misogyny, racism, colonialism, death
I'm unsure of what is meant by Narrative Game, so take the following with a grain of salt, please. It's some mechanics of games that I would call indie rpgs and that, I think, are sometimes called narrative or storygames, also:
A token economy
In Avery Alder's Dream Askew I gain tokens by playing towards other characters' strengths or by being vulnerable with my own character. I can then spend these tokens to bring my character's strengths to bear. She writes that this is supposed to "create a narrative rhythm." Another interesting example of this is Technoir, a rpg by Jeremy Keller. There, certain dice double as tokens. Players spend them to make a lasting impact on GM characters giving them to the GM, who in turn spends them to have their characters go after the players'. Fitting for a rough, Noir-style game. Robin D. Laws' DramaSystem (Hillfolk) has a character be the petitioner and another the granter for most scenes. The petitioner seeks an emotional reward from the granter. If it is refused, the petitioner gains a token, if the granter willingly gives, they do. Laws writes that this "bend[s] events toward a satisfying literary rhythm, where characters sometimes prevail and are sometimes defeated in emotional confrontations." Another interesting use of tokens is as a timer, basically. Vivien Feasson's Perdus sous la pluie (Lost in the Rain) is a horror rpg where every player starts with ten tokens and once they're gone, their character is lost. Aside from the horror aspect, these tokens also model a sort of group dynamic, where I lose tokens for being pushed out and made to feel alone, but everyone can always give away one of their own tokens to another player, too, for comforting their character. Or lash out and hurt another character, losing a token, but making the other player lose one, too.
Judgement
In Danielle Lewon's Kagematsu, a rpg about a group of women trying to sway a wandering knight (who must be played by a woman) to promise to save their village, the knight's player has to secretly decide whether the attempts of a villager to win the knight's affection are met with love or pity. Without love, things become very desparate for the villagers fast, so this choice matters a lot. In Bluebeard's Bride, a horror rpg about the fairytale, the GM presents the Bride, the single main character of the game, with rooms in Bluebeard's mansions and objects therein that the players may ask questions about. To leave a room, a player must basically tell the story of what they think happened in there, gaining a token of faithfulness if they clear their husband's name or of disloyalty if they reveal him as a murderer. How hellish a choice that is, is a big part of the particular, feminine horror of the game. A combination of both a token economy and judgement can be found in Liam Liwanag Burke's unmatched Dog Eat Dog, a rpg about colonialism. After each scene, the player of the Occupation force that is colonizing the Natives must make a judgement as to which Native player adhered to the rules and who broke them, the first and foremost rule being "The (Native people) are inferior to the (Occupation people)." Natives gain a token for adhering to, and lose a token for breaking one. Then the Native players make up a new rule based on their interactions with the Occupation and what behaviour was modeled or punished. So as a Native player you keep making these choices for your character like where you go, how you talk to people, what rituals you keep up, who you get involved with. And apart from the fact that every one of those seemingly small actions can get your character killed if the Occupation feels like it, what you feel and maybe even fear most is how, slowly, interaction by interaction, day by day that you spend under this regime, your character begins to drift in a direction where you might not want them to go. As a consequence of how your actions are perceived by the Occupation. Because if you run out of tokens, your character runs Amok and has to die whereas tokens gained mean your assimilation. As one reviewer put it: "Dog Eat Dog isn't a game about how colonialism steals resources; it's a game about how colonialism steals identities."
Conditions
John Harper has a nice description of conditions in his game Lady Blackbird: "A condition constrains what the player should say about their character. It’s a cue to tell the GM and players to pay attention to that thing and use it as material for the developing fiction." So if your character has a Condition like Trapped or Angry that aspect is put into focus. In Avery Alder's Monsterhearts Conditions are always social perceptions, the labels other people put on your character. In Gregor Hutton's Remember Tomorrow there are Positive Conditions, too that can be gained and traded in for mechanical success. From a design perspective having a fixed set of Conditions (or in the case of Monsterhearts Conditions of a certain nature) is ensuring that certain situations will have weight in the game and pointing people at them. In Remember Tomorrow, where Positive and Negative Conditions come and go very quickly, they also keep characters moving.
Replaying a scene
A pretty unique mechanic can be found in My Daughter, The Queen of France by Daniel Wood. There, the same scene can be played over and over again. That means that the group can revisit a scene later, knowing more about a character's motivation, and see how that changes things. I feel it's a very interesting method to give depth to characters. Also, there are certain limitations that gradually get removed. For example, only when a scene is played for the third time is it allowed to play out or describe emotional states. So that is something that people really build towards.