What you are describing is basically an application of game theory with a single game being played vs multiple games in repeated encounters.

In the video game there is anonymity and single unique encounters: see a player, kill him, loot him, move on. This results in chaos because it is an environment with no stability with everyone for themselves. Same with driving. Everyone has an incentive to drive like a prick to make themselves better off, even though everyone collectively would do a bit better by everyone following the rules.

The trick is...for the individuals they're familiar with and they feel similar to

This is describing a game with repeated interactions where your actions have consequences in games played later.

If you play a game (a single interaction) then your best strategy is to defect, meaning, be an asshole, break the rules, loot everyone, move on.

If you play a game with repeated interactions over and over with the same players (friends, family, colleagues, business partners, foreign policy with other countries, and so on) your best strategy is to cooperate, play by the rules, and do best for everyone.

I participated in an experiment of this during undergrad. Twenty or so of us were put on computers to play a game, something to do with trade. If you defected and broke the rules you could make double. BUT, all the players in the game had complete information, so if you double cross player A, player X would see that and not do business with you. Within a few rounds we had all figured it out, everyone cooperated, everyone traded with each other, and everyone made a ton of money. The few players who were assholes made a good score off the players they cheated, but they made way less than everyone else who cooperated with each other long term.

If you want to read more you should google things like game theory, game theory N person games, prisoners dilemma, nash equilibrium, things like that. This is a good start: https://www.britannica.com/science/game-theory/N-person-games