There should be a term for the first time you play a story-focused game, before you really get the hang of how to decimate all your enemies, before you know what’s going to happen in the plot, before you fiddle with the “moral choice” mechanics just to laugh at how big a jerk the protagonist can be, or before you find out that the choices you make don’t even really matter at all. This experience relies on a blend of story-oriented and mastery-oriented appeals, where the challenge of the game heightens the sense of drama and tension in the story, and vice versa.
I don’t know what the term for this type of play should be. Personally, I’d like to see it become more the norm for games with narrative pretensions, but it’s tough to pull off. Even story-oriented games seem to have a hard time pulling it off. And, notably, it’s usually absent in replaying a game. I’m not sure it has to be, though.