I don’t mind the nit on word choice but in my mind a game becomes a sport by the existence of a Championship match and title.
Also, I think this follows how most sports come to be. They are started as child play, when we have the time/leisure/energy, then they eventually become something some of us want to continue with as adults and the rest of us will pay to watch because we enjoy the sport so much (often fostered during youth play).
There are dozens of sports that I have no interest in simply because I wasn’t exposed to them as a kid. As an older American, we did not play Soccer(football) when I was a kid. It’s pretty popular now and my kid has had me go to professional games and such but I still just don’t really understand the game/rules/strategy or fully appreciate the difficulty of things that occur. I could learn I suppose but I still just have little effort in doing so as a middle aged person. I could say the same about Cricket and a handful of other sports that I never played as a kid but know are popular elsewhere. Likewise, when people move to the US, it usually takes them a while and likely never fully get into American Football and Baseball. Basketball has become more global and so I do expats that follow that sport. More likely than not, they follow the sports that interested them as a kid and just live with the time zone issue.