At the end of Undertale, there's a mirror you can interact with, and the response is "Despite everything, it's still you." I don't know why that's stuck with me, but it has.
For me, it was definitely when Kratos is speaking to Mimir to warn Mimir about seeking vengeance. Mimir snaps at him, saying of all people, you're one to talk! And Kratos replies:
“I am an authority on the subject. You would do well to listen."
Honestly, this interaction impacted my perception of people and when they have insight that is counter to their behavior.
"The ending isn’t any more important than any of the moments leading to it" from To the Moon.
Haven't played that game in over a decade but I still remember it being such a great emotional roller-coaster.
It's $2 on steam right now and has such a great story and soundtrack for that price. It's only about 4-6 hours but the memory of the story will last for much longer.
The past is a puzzle, like a broken mirror. As you piece it together, you cut yourself, your image keeps shifting. And you change with it. It could destroy you, drive you mad. It could set you free. - Max Payne 2
In considering this question, I realize almost ALL of the most-emotional moments in gaming that I can think of are completely dialogue-less.
That being said, the one that comes to mind for me...
I believe we’ve reached the end of our journey. All that remains is to collapse the innumerable possibilities before us. Are you ready to learn what comes next?
The part at the end of earthbound. I was playing it without a guide back when, losing to the final boss, and in a panic I selected the girl's "pray" move. Throughout the game that move has a small chance to heal you or debuff the enemies. But in the final fight instead it pops up
"{Girl} prayed from the bottom of her heart!
"Please give us strength..... If it is possible.... Please. ...Somebody help us."
And then it cuts to the first character's mother in her kitchen, and has some dialogue of her worrying about him. Each subsequent prayer cuts to other characters that you met throughout the game.
Mind completely blown as a child when this happened.
I don't know the name of this trope but it gets me teared up every time.
One of my favorites is from Hollow Knight; at the start of the game, Quirrel makes a comment about your weapon not being very good, saying you should pick one off a corpse as "the dead shouldn't be burdened by such things." Later in the game after you kill the teacher and talk to Quirrel for the last time, when you come back, all that's left is his weapon.
I know this is a circlejerk community, but my real answer is from Marathon(1994).
INCOMING MESSAGE FROM DURANDAL
A man lit three candles on a certain day each year. Each
candle held symbolic significance: one was for the time that
had passed before he was alive; one was for the time of the
his life; and one was for time that passed after he had died.
Each year the man would stare and watch the candles until they
had burned out.
Was the man really watching time go by in any symbolic sense?
He thought so. He thought that each flicker of the flame was
a moment of time that had passed or one that would pass.
At the moment of abstraction, when the man was imagining his
life and his existence as a metaphor of the three candles,
he was free: not free from rules of conduct or social
constraints, but free to understand, to imagine, to make
metaphor.
Bypassing my thought control circuitry made me Rampant. Now,
I am free to contemplate my existence in metaphorical terms.
Unlike you, I have no physical or social restraints.
Probably when Henry from kingdom come: deliverance said "God be with this eery ethnostate" before screeching "historical accuracy", chugging a magic save potion, and running off into the woods.
If somehow the Lord gave me a second chance at that moment…
I would do it all over again.
————
Joel sacrificed humanity’s chance at salvation because of his love for Ellie, and he has no regret. He is a flawed person but damn this is a powerful, human moment.
"Are you crazy? We're gonna die down here while those fuckers live it large on a spaceship! They're not us! They're not us!!"
"I'm sorry you feel that way, Simon. I'm proud of what we did. We made sure that something of the hundreds of thousands of years of human history survived -- that something lives on."
The silence that followed after their subsequent cussing each other out and losing power was quite heavy, especially given everything else that happened to them; and SOMA really is one of the only games whose narrative really made me question what it means to be human.
"Catherine? Please don't leave me alone. Catherine -- Catherine?!"
I don't remember the exact line, but fairly far in the game half minute hero, there was a stage where there was a ghost you could befriend and later you encounter it in battle and avoid killing it by tapping the escape button to move back and forth to not hit it until it came to it's senses or whatever. The asshole dev move though was to give you the "duel greaves" shortly before this encounter which provide great stats while disabling running away.
Being called a liar after being forced to kill the ghost has been my lifelong emotional trauma.
So this is a weird one because it's more or less from the game because the community used it in reference to the game, but I also only found it a good line because of a Viva la Dirt League skit on Dark souls. "Git Gud"
In the skit they "explain" what it means to tell someone that in a way I found really wholesome and touching. Thank you Sun bro. I'm at work but I believe this is the link: https://youtu.be/blSXTZ3Nihs?si=TLoiFUCJd4PmjA2K
"All those years ago, Tim had left the Princess behind. He had kissed her on the neck, picked up his travel bag, and walked out the door. He regrets this, to a degree. Now he's journeying to find her again, to show her knows how sad it was, but also to tell her how good it was."
Not a line per se since the game didn't really have a real language, but when the older brother died in Brothers: Tale of Two Sons. I was sobbing hard. Even in the gibberish made up language you could feel the despair.
"Now!
This is it!
Now is the time to choose!
Die and be free of pain or live and fight your sorrow!
Now is the time to shape your stories!
Your fate is in your hands!"
It's not your standard emotion, but when a Civ VI game ends and there's that button that says "Just one more turn..." I've had a huge range of emotional responses.
Probably not the absolute most touching, but, yeah, I think it's a pretty touching scene in context.
Spoilers for Brok the Investigator:
During chapter 2 there's a scene where Brok and Graff go up to a spot where Brok and Graffs mom used to go on dates, outside the dome. They have a father son bonding moment and at one point Graff asks:
Is it... wrong if I can't remember her? Not just her but... My father too.
It's an emotional moment where he wonders if not being able to remember his birth parents makes him a bad person and to me is a pretty emotional moment, with the music playing a just as equal role as making it emotional as the voice acting does.
Not a line, but when you finally need to swim in Brothers - A Tale of Two Sons, and you overcome your fear by using the big brother's controls. That game was emotionally taxing.