I never met Conway myself. But I first encountered his Game of Life in a science fiction book I no longer remember the title of. The book didn't make much of an impression but the game did. I played it out on paper during long car trips and when we got our first computer the first code I ever wrote that wasn't "hello world" was an implementation of Conways Game of Life in gw-basic.
In a way his game helped start me on the path to the career I have now.
For me was Calculating God by Robert J. Sawyer, in which an alien appears at the Royal Ontario Museum and asks to speak with their paleontologist. Through that book, GoL was my on-ramp to all kinds of cellular automata, a-life, and procedural generation techniques that I still find fascinating.
My recollection of conway is that he was quite good at backgammon -- good enough to make a bet to swap salaries with a lecturer over a public series of 30 (or more) games held in the common room. I believe that he won by one.
When I played with him we enjoyed the game, so it's not clear he was playing to win. Actually, it was clear ... he was not playing to win, he was playing to have an interesting game.
I'm sure he could have played seriously and thrashed me, had he chosen.
Years ago, I was sitting next to John Conway and another older Professor in a small computer lab in Fine Hall (Princeton's math building) while waiting to meet my advisor. What I remember most about listening in on their conversation was how much fun it seemed they were having. Especially Conway. It was like he was engrossed in a really fun game and was trying to come up with new ways of thinking about the rules. I think you can see that in his work too.
The pure joy he took in his work is something I admired.
Stood up a page on my website for this, got my parents running the game a couple times, and they commented: looks like how coronavirus spread.. Such is life.
I was President of the Liverpool Mathematical Society for a year, and maintain a connection. I only knew Conway when I was at Cambridge, 1983 to 1987, and at the time didn't know of his connection with Liverpool.
https://youtu.be/xOCe5HUObD4
It really puts some of these mathematical problems into perspective when you think about how they can span multiple human lives.