I still remember some of the games we played on cheap Russian handheld consoles back in the mid 90s. Tetris and snake, but also a racing game that had the same mechanics like Tiny Ski, except upside down and with the logical game board three blocks wide. I had a lot of fun with that racer; I can picture it in my mind more vividly than most of my adult memories.

The three games I mention definitely cross the "affecting life" threshold, in the sense of becoming a small part of the culture - I could ask Polish people my age about these games, and many would remember them. But they didn't become part of the culture because of their mechanics being good in the absolute sense. They did because of availability, context of play, and their mechanics being good compared to other games available at the time.

Were Tetris to come out today, people would look at it, think "what a boring, shallow game" and go back to Candy Crush or whatever is currently the hottest casual.