I saw this Lemmy post, but a huge list of games with no discussion isn't very interesting! Let's talk about why the games that influenced us had such a big impact - how they affected us as people.
For me, it was the PC game Creatures. It's a life simulation game featuring cute little beings called 'Norns' which you raise and teach.
You can almost think of it like a much cuter predecessor to The Sims, but which claimed to actually "simulate" their brains.
As a thirteen-year-old it was the first game that made me want to go online and seek out more info. What I discovered was a community of similar-interest nerds hanging out on IRC chat, and it felt like for the first time in my life I had "found my people" - others who weren't just friends, but whom I really resonated with.
I learned web development (PHP at the time!) so I could make a site for the game, which became the foundation for my job in software engineering.
And through that group I also discovered the Furry community, which was a wild ride in itself.
So yeah, Creatures. Without that game, I think I'd have become quite a different person.
Mafia 1. Not only is it still one of the best single player storylines, it's also how I "met" my best friend. My family had just moved between cities and I had to change schools. I obviously didn't know anybody yet and joining a class with existing social circles can be hard. The first common ground I found with someone was this game, as we both had played it and struggled with the same mission ("The Race" iykyk). We hung out after school trying to beat this game together. This is essentially how our 15+ year long friendship began.
I also really got into classic cars because of the game and my future hobbies and career would most likely have been very different had I not played it.