Frostpunk

I never had problem to send my virtual people into their early demise in lot of games and genres, but for some reason getting to decide between two bad options, and doing it so time after time, while the temperature is getting lower and lower leading to more potential deaths, was quite nerve wrecking experience for me. Loved the game, it was my favourite from 2018, but it really did a number on me.

Nier Automata is such a damn good game.  One of my favorites.  Great call out.  

A couple more for me:

Sakuna: Of Rice and Ruin

As you play through the game you forge strong relationships with unlikely friends. You’ll share many moments and meals together.

Spiritfarer

This is a heavy-but-cozy game where you bring the spirits of the dead to their final resting place. Before that, though, you’ll have the chance to live beside them, feed them, hug them, love them. I cried several times.

I also realize now that all the games I listed share something in common: living together. Natsu-Mon, Animal Crossing, Sakuna, Spiritfarer — in each game you spend weeks living alongside your neighbors and friends. Heck, in New Horizons I’ve spent 4+ years living alongside them

I suspect that’s what makes them so meaningful to me.

I forgot about The witcher 3. It hits every beat along the journey you go on and really pulls you in andnm tugs on your heart strings. Even the little side stories are emotional. RDR2 might hit more strongly but it's mainly depression inducing. The Witcher 3 hits often and softly and it's a 150 hour journey if you have the DLC so the investment you feel in the world and with the characters is strong. If it had as many character deaths like RDR2, it'd send you into hospital in a state of Catotnic shock.

Persona 3-5, Metal Gear Solid 1-4, Yakuza Games, The Last of Us.

Big emotions and iconic story moments with fantastic characters have greatly enriched my life.

Anime has perfected it, but video games can be very strong at it too :)

I second this, Neir Automata started with pure vibes and evolved into a damn heart wrenching story. I put it down to a perfect OST, without that it wouldn't have hit as hard. 

There aren't many games that I remember for emotions (aside anger. frustration and eventual joy of victory).

I call Mafia 1 the game with best story that I've played and the revelations near end were shocking, that those things you had done...

Cult of the Lamb, Fallout New Vegas, WoW, MGS 4, Bioshock 1-3, are a few that come to mind that move me in different ways (from making me care about the characters, to wanting me to see the deserved downfall of the antagonists, or caring about another character's wellbeing).

Cult of the lamb has me caring for my flock on a daily basis (I've married multiple followers, but I keep 2 distinct ones closer to me), keeping them well fed and breaking up fights between other members.

Fallout: New Vegas has me caring for different factions, but usually it's those within, like civs caught in a crossfire, or those unfortunate to what fate has dealt them.

WoW: generally heavily invested in the lore of that game. Despite having fought for the Horde for many years, I still held onto some compassion for the Alliance faction, so when I saw their world tree burning to a crisp, all the women & children that perished within it, I felt nothing but disgust, and a desire to see Sylvanas Windrunner & the Jailer pay for their crimes against life.

Metal Gear Solid 4, pretty much ended up caring about nearly everyone in that game, from Drebin being used as another cog in the machine just to live a life, to Ocelot having to live a completely fake life, just to finish a mission given to him decades prior. Snake I have always cared for, mainly because he was born/created as nothing more than an "anti-agent" against another man who wanted to enact Boss's dream and mantra (I also believe in the "world without borders" philosophy).

Bioshock 1-3 had me caring for what happened to the multiple diaries of other Rapture civs. I actually cared for the big Daddies, despite them opting to kill you if you ever tried to steal their little sisters, they were still once human and experiment against their will, so I still feel for them (not the splicers though, they act more like drug junkies and resorted to violence at will, as well as falling for indoctrination).

The entire Halo franchise takes me back to my days as a space Marine and triggers my PTSD.