I'm going to echo Bastion as well, since it ties in a narrator with player actions and does it really well. It's a good way to get a slightly reactive narrative based on player actions.
I'm also going to throw in Braid, because that story has some great revelations and it ties into the mechanics pretty well.
I'd agree with Planescape: Torment, but that will likely have accessibility issues to anyone of high school age. It's got dated graphics and practically no tutorial to speak of, plus it's based on old AD&D rules. If your students can get past that then it's got a fantastic story and some really good character interaction with dialog choices and consequences, but it may just be getting a bit old.
Deus Ex as well, but that's less of an issue as it looks better graphically and it's easier to grasp its mechanics because it doesn't rely on a dated rule system. Generally if you have a section on player choice and agency Deus Ex is the way to go. The great part of it is the gameplay actually can affect narrative, so it doesn't all boil down to conversation choices like most Western RPGs. You can do a compare/contrast with another T rated Western RPG like KotOR, but I think Deus Ex beats it out in terms of narrative, especially when it comes to player agency and gameplay.
For more traditional narratives that are a bit more linear, I'd say Psychonauts is really good, and it handles some mature themes in a tasteful and subtle way. But it'd likely be a great thing to discuss with a class. Beyond Good & Evil is up there, too, and follows a similar pattern of approaching some mature themes subtly. The Longest Journey as well if you think your class would be okay with a point-and-click adventure, which I hope they are because TLJ is fantastic.
A lot of JRPGs would probably be good too, but those are more straight story and less narrative. Still, if you want to change pace and want to showcase some good linear storytelling there are lots of great titles out there. Any of the recent Persona games, Lost Odyssey, etc.
One thing I definitely think you really should include is The Stanley Parable. A few others have mentioned it, but it's one of the best commentaries on game storytelling I've ever seen, and it all takes place within a game. It doesn't judge or preach, it just explores ideas, and it's phenomenally done with a great VA as the narrator. The only thing is you'd probably have to have it be one of the last games you cover in the course, as its nature of exploration of narrative requires you to have some experience actually experiencing narrative in other games. It relies on things we take for granted in games and if you have any students new to gaming they'd need to get used to some of the tropes before they could see what The Stanley Parable does to deconstruct them and point them out. Still, it is definitely one of my favorite things that I've "played" and I'd highly encourage anyone interested in game narrative to give it a shot. Play through all the endings and see what you think, it's a really short process but has a lot of potential for classroom discussion.
Edit: After reading psicat's post I'm going to echo Sanitarium (another point-and-click, I think TLJ is better but Sanitarium is really really good) and Anachronox as well. Anachronox is hilarious and has some great satire to it. But it too relies on knowledge of some tropes to really get its humor, so where it fits (or even if it fits at all) really depends on where you're looking to take the class.