Player character is a holdover term from pen and paper roleplaying games, where play is like a form of moderated improvised theatre. But in videogames there is no such thing as a player character.
Players project into roles, which means functionally clear identities whose relationship to the game world is easily contextualised. They control dolls, which means any physical entity within the game world. Dolls which leave the player’s control (whether permanently or temporarily) become characters. Characters which come under the control of the player become dolls.
The reason there is no player character is that the player does not become the entity that she controls. She is not an actor taking to stage, but more like a driver or a pilot: The doll becomes an extension of her.