Even if we account that "narrative game" is something of an exonym that is frequently imposed on games, there are probably things about these games that get them labeled as such, even if by their detractors. Note: these qualities may be found in other "non-narrative" games too, but it's often a combination of these things. Likewise not every game that gets labeled a "narrative game" will have these things or to the same extent.
These games often include, but are not limited to...
- ..."Fiction First" Principles, Rules, and/or Mechanics
- ...an interest in the fictional stakes and/or consequences in conflict resolution
- ...a mechanical interest in the dramatic beats of the player characters and/or fiction
- ...a greater concern for Emulation > Simulation
- ...ways for players to declare narrative truths or story details in the fiction
I will add that for some people I have interacted with here, it only takes the below to get labeled as a "narrative game."
* ...a game that has any mechanic that breaks their idiomatic sense of in-character roleplay immersion