Episode 2 of the first Life is Strange. That still has had more of an emotional impact on me than any other game in memory. Granted my memory isn't great, but of the plethora of games I've played over the last 30+ years I've been gaming, the ones I remember, are the ones where it gave me a real emotional reaction. The end of that episode, with the events as they had built up, and what was on the line, and how genuinely worried I was if things went badly, yeah, that really hit me. I remember feeling the stress acid feeling in the pit of my stomach, like when I am in genuine tense situations. My skin got prickly as my hairs stood up on end, and my hands were shaking from the anxiety of it. I remembered enough to notice all this, as I was carefully making my choices based on what I knew, and when I got the result I was hoping for, I remember the feeling of genuine relief wash over me. The only other game I can remember doing that for me, was the first Homeworld game, for multiple reasons. But yeah, I remember sitting there in the resolution scene of the game, taking stock of the actual, physical response I had to it, and how much I enjoyed it. To be so invested in a story, that I actually gave a shit, and had a physical response to it, is one of the reasons why I have played video games my whole life.
The God of War reboot(ish). That game just made everything I enjoyed about the previous GoW games better, and dealt with the stuff that pissed me off in that franchise. I had a really hard time with GoW 3, as by that point, I wasn't playing a dark protagonist, I was playing basically Anakin Skywalker in Revenge of the Sith, once he got to the murdering a room full of children point in the story. You're basically the antagonist, and you are such an asshole about your rage boner to kill the gods even if it destroys the world, that I just didn't empathize with Kratos anymore. I wasn't having fun playing him anymore, because he was just a monster, a homicidal jackass, and I'm not the kind of person who enjoys playing badguys. I don't find it cathartic, I just find it unpleasant. So then the new GoW comes along, and actually addresses his past, and shows that he has realized "Wow, I was a fucking asshole, I should probably not be like that anymore." And then had to deal with his past, while raising his son. Was just fucking great. Plus, the level of epic battles were on par with the insane stuff that happened in the previous games. The literal EPIC things Kratos and Boy do, I was just giggling, especially when I was able to figure it out ahead of time. I remember one scene where I was like "Oh, yeah he's going to just go up there and shove that entire massive thing down. Why? Because Kratos." And sure enough, that was his undisclosed plan. And it was sufficiently epic in scale.
Lets see, what else. Uh, I guess probably Human Revolution, and Mankind Divided. I really enjoyed those games, even with their flaws. The tone and mood of them, the transhumanism and cyber-futurism just really ticks all of my boxes of deliciousness. Plus the fucking soundtrack to those games was mind blowing. I've since bought several of Michael McCann's albums just because I love his sound.
There's probably some others, but those are the ones that come to mind at this moment.