Here's how I know snooker isn't a sport. Back when I went to state school in Perth, there were always at least a couple of kids who would "opt out" of the weekly school sports triple period. They'd bring in a sick note to get themselves excused, or they'd choose to walk the 400m instead of running it like everyone else.
As we got to round year 10, more and more students would take this route, probably just because 15 year old teenagers are that much more pissy and hormonal than 10 year old ones. To manage this dynamic, the school introduced snooker, archery and low key activities like that (probably knitting these days, knowing Gen Z) as "sports electives" for the year 11–12 school years, and most of the "sports rebel" kids happily jumped on those wagons. So ya know … that's how I know they're not sports.