I would say activity is a huge encapsulating word that all sports, games, clubs, etc fall under.

Sport to me is an intensive competitive activity.

I would like to also say team based, but wrestling, track, and swimming would be absent from such a definition. Similarly, if you were to say outdoors most winter sports would be excluded.

With my definition you could argue for games like Chess to be intensive and competitive. I’m unsure. I think it changes depending on the level of play. At the end of the day, the only people who really care about exact definitions are those in administration deciding what activity gets what.