Probably an obvious one, but Life is Strange was a pretty emotionally fraught game to play through. Everyone's probably aware, but it is filled with choices that determine lots of different small outcomes as well as the main ending. So after I finished it, I spent the evening watching streamers react to the ending and sniffling along with them.

Personal story about that, a good friend passed away unexpectedly right before the pandemic, and his wife asked for my help finding some things on his computer. He was a great guy, big burly dude not known for being overly-sentimental but a wonderful imagination/DM. As I was going through stuff she was reminiscing about him. So we opened his Steam library and he had 2 games installed. Fortnite and every chapter of LiS. She had no idea what that game was, but imagining him secretly huddled over his laptop, guiding Max & Chloe along just broke me.

Another game that drew me in instantly was Hellblade: Sennua's Sacrifice. Seeing the character's backstory in the first couple of scenes and knowing that this was a story game dealing with mental health and loss was major, and I was immediately motivated to help her get through the healing process.