As others have mentioned, it's not about the game, but specific experiences you had. I have memories of intense stand-offs when rescuing hostages, or the one time I had an __absurd__ streak of luck and managed to single-handedly wipe out the entire other team (never since repeated).

Some of my strongest gaming memories are of the first (?) level of Rogue Spear (one of the Rainbow Six games), where I was hunting terrorists in the Met. It was fifteen years ago, but I still remember how upset I felt when I saw a virtual character fall down after being shot, and I can still remember the intense despair that crushing my elation when a hostage panicked and ran in between me and the terrorist (and I shot him). I played that level so many times that I can probably still sketch the map. I remember nothing else about the game, but the experience of playing that one map stays with me.

This is a completely different kind of "story" or memory than one's going to get from a game like Borderlands.

With all due respect, it doesn't sound like the simulated violence had much to do with the nostalgia you're describing. Not that I don't believe that violence can't be a tool used to evoke empathy, but effective stories can certainly be devised without hyperrealistic violence.

Story in the sense a game of football has a story.

As per what he said there is no "Story of Counter Strike" and that is what he likes about it. It is a framework for him and his team mates to invent a story of struggle told in near misses and heroic wins.

Why he has trouble inventing the same stories with robotic team mates and opponents I am not sure, but he seems to find value in the shared experience.

I think by stories the author means real adventures with you and your teammates for that specific match - not some sort of CS lore. Each match brings new humans that will play, react, chat differently then an AI in a single player game.