I'm old and have enjoyed many, many games over the years. However, the one that hit me hardest in the feels was The Witcher 3. The ending where Geralt realizes that he has to let Ciri make her own decisions, scary as they are... wow, it was so well done. It's one of the best examples of how a game can become art on the same level as cinema and literature.
Edit: I want to add another. The first game that made me feel actual dread was the original Quake, especially when played in a dark room. The soundscape was incredibly immersive. I remember literally moving my own head to try to peer around corners.