Metroid Prime 2.

That game was tough as nails and I never gave up on it. Came out when I was 14 and I still go back to it every few years and realize that it formed my basis for never giving up on things regardless of how tough they may be.

Cliche as fuck I know.

This might sound crazy, but the first game that came to mind is Disgaea 5.

And it wasn't the plot or the fantastic music. It wasn't a main character. It was just a regular fighter class character.

Wild Cry Increase stats by adjacent enemy unit x 15%. Rank 1 Unique

His rank 1 passive ability makes him significantly stronger the more enemies are near him, to stand up to danger and fight it head on is inspiring.

Shaking Excitement Increase stats by enemy units on the map x 3%. Rank 5 4

Even more inspiring is his rank 5 passive ability (late game). The more enemies he has to face, the stronger he gets. I often equate Shaking Excitement with myself. When I have to face troubles head on, I don't get anxious, I shake with excitement. When the problems are many, I must get stronger to knock them all out of the park.

He also has a quote "I want more!" (English Dub) Which I also took for myself, I don't want to sit idle and stop improving. No, I want more in life. I don't want zero challenge, I want more!

In addition to this, it is a mere coincidence. But in the first Disgaea game me and my friends really enjoyed it and would name characters after each other. The Fighter class was dubbed with my name, so as a tradition I always name my first fighter class in Disgaea games after myself.

I have found many games very moving and emotionally appealing, but very few have made an impact regarding my way of thinking about myself or others or the world around me. It's one thing to be moved by something, and another to be inspired to really self-reflect and maybe even - dare I say it - grow as a person.
I won't spoil anything, I'll just describe things in more general terms. Three examples that I can think of:
The Uncharted series. The relationship between Nate and Elena has had its ups and downs throughout the games and at times, they have struggled. Sometimes Nate has been so consumed by his need for adventure that he has not been the most devoted partner to Elena. I see myself in him a little and my own relationship failures have been largely due to my neglecting my girlfriends just a tad too much. Some of the scenes in those games have hit me pretty hard, actually. I've had to face my own inadequacies as a partner and think on them.
God Of War (2018). The slowly developing relationship between father and son is really touching in this one. I actually have a great relationship with my son, but this kind of thing gets to me so easily. It's so important. Kratos' parenting style also made me question if I'm being a bit too soft on my boy, will he be able to hack it in this world once he's out on his own, or should I try and toughen him up a little? (Just kidding :D)
The Last of Us Part 2. Part 1 was an excellent game as well, but the sequel was just something unprecedented. Obviously a very divisive game, you either fall in love with it or you hate it with a burning passion. I am of the former group, the game totally blew my mind. It could have gone the safe route of giving us more of what we wanted based on the first game, but it chose to give us what we sorely needed instead, and this did not go over well with many fans. Emotionally, the game took me from the lowest lows to the highest highs and everything between. It also did what no other game had done before, it changed my perception completely. Turned it around in ways I thought was not possible. It taught me things about myself and how I relate to perspective and empathy, how those things are interrelated, and overcoming overwhelmingly negative emotions, to break through to something new. I surprised myself, the game made me do it. I know this sounds very vague and hyperbolic because I'm avoiding spoilers, but I really think it made a better person. Just a tiny little bit better, at least. Of course it's perfectly valid to hate the game, and some of it was actually intended. They wanted to elicit all these emotions out of us, they took a risk and for some people it didn't pay off. It's a shame that the leaks came out and some people wrote the game off without actually going through the experience. They might have surprised themselves as well.

A couple games, that shaped me in different capacities and ways. Obviously, all pretty old by now and a long time ago, and I mentioned them and how they impacted me in the Top 50 thread.

Duck Hunt (NES): Likely the first video game I ever played, played a lot with my cousin at my aunt's house, an avid gamer at the time while I just wanted to go to the playground instead.

Soccer (NES): Another game I played a lot with my cousin, opened me up to competitive gaming.

The Legend of Zelda: A Link to the Past (SNES): The intro to this game, where it rains outside, made a lasting impact on me and is thus one of the most influential games on my personality. The intro was the most epic thing I ever saw at the time, and instantly made me a gamer, and Zelda my favourite series for the rest of my life. If my aunt hadn't shown me this game, I wouldn't be gaming, in any capacity more than a casual one, today. Maybe I'd even have played sports, can you imagine.

#14: Gunfighter (Showdown in 2100AD) (G7000/Odyssey2): Simple arcade game on an old 2nd Gen console my mother dug up from the attic, made me appreciate there were more manufacturers and more types of games out there, this broadened my horizon.

Star Wars Rebel Assault 2 (Mac): My introduction to Star Wars and the first game I played on a home computer, after my new stepfather bought our house our first computer. Star Wars would become my favourite media franchise, and I watched the movies and everything else because of it soon after.

Step-On-It (Mac): Obscure puzzle game from an obscure developer on Mac computers, a clone of the NES's Solomon's Key. The game made me appreciate challenging, puzzle and problem-solving oriented games, pushing towards certain genres and series in later life.

SimCity 2000 & SimTower (Mac): Played simultaneously and had a cumulative and severe impact on the course of my life. These games, with SimCity 2000 later being replaced by 3000 and 4 on Windows PCs after it, sparked my interest in architecture, city building and construction in general. This made it so I went on to study architecture later in life, and become an architect. These games had the biggest impact on the course of my life of any, and I wonder how my life had gone, and what I would be doing now, if I never played SimCity and SimTower.

Mario Kart 64 (N64): This game has a lot of emotion attached to it and probably has the most memorable play session of all time for me, because it was the last game I played together with all my family, until drama and worse made it so most of those I played with aren't around anymore for various reasons.

Anno 1602 (PC): I played this, and still play the game's successors with my best friend, and while our friendship was already long and strong as it started on the first day of school, this game probably cemented it for life.

Chrono Cross...I now question reality and everything that may or may not exist.

I'm kind of sad now because I can't think of any game that actually changed my views on the world and life. I have many games that are very dear to me but not really influenced my life. I think the closest to that would be Mega Man X5 and Sonic Adventure 2, which probably shaped my love for kinda-edgy anime designs.

Ever since I played Animal Crossing GameCube as a child I've been excited about owning my own home, having a good relationship with neighbors, and living a debt free life style. That's a pretty big influence! I do two of those well and we are well on our way to paying off debt based on decisions we are making now as a family.

Gitaroo Man actually inspired me to try real guitar.

Shenmue massaged the idea into me that revenge is a dead end street. Also, life is pretty mundane but the moment is full of Beauty and wonder. Not to mention the realization that days get repetitive unless you are reaching your goals.

Metroid had convinced me that isolation was not only ok, but cool. Then Halo CE proved that co-op is the real way forward.

None have really shaped me as a person.

I like Role Playing Games, Strategy Games... Which is far removed from anything else in my daily life.