Narrative games are basically dialogues between the game and the player. The player tells the game what choices their character makes and the game tells the player the outcome of those choices.
The choice of perspective decides what roles the player and the game are playing.
In first person perspective, the game becomes a dialog between the player and the character.
Player: Larry, open the door!
Larry: I can't. I am too afraid.
The player is not so much interacting with the world, but rather interacting with the character, who is interacting with the world.
This perspective is useful if your narrative is mostly carried by the personality of the main character. It even works when the personality of the main character is very different from the player.
This perspective also allows the player-character to talk directly to the player. The character can tell the players their thoughts and opinions without filtering them through a narrator or even argue with the player.
In second person perspective, the player becomes the protagonist while the game takes the role of the narrator:
Player: I open the door.
Narrator: You are too afraid to open the door.
Now the player is the main character. The character's actions are the player's actions and vice versa. This gives you the highest grade of immersion in the story. So if immersion is your primary goal, then this is usually the best perspective.
Unfortunately there is a downside to this style: It can become uncomfortable when there is a dissonance between what the player wants to do and think and what the game makes their character do and think. Tell the player: "You really enjoy performing this immoral and despicable act" and the player will react: "WTF game, what kind of person do you think I am?!?". There is always a limit to how much agency you can give to the player in a game, so such uncomfortable situations are hard to avoid completely. Not unless you want to leave the interpretation of what's happening in the game completely to the player.
So this style almost requires that the player-character is a) a blank slate with very little personality so everyone can easily project themselves into them or b) a character your target audience can identify with extremely well.
In third person perspective, the game becomes a discussion between player and narrator about the player-character:
Player: Larry should open the door.
Narrator: Larry considers to open the door, but he is too afraid.
This perspective creates the largest distance between the player and the character. The player-character becomes yet another character in the story.
This is useful if you do not want to focus on either the player or their character and put the focus on the secondary characters and their interactions with the main character and each other instead.
It is also useful if there is more than one controlable character in the game. When the player never really enters a character's mind, then the shock of currently being in the mind of another character feels less severe.
