The surprisingly emotional debate of "is it a sport or is it a game" has been around from the moment we invented the category of "sports". I don't think it will ever be definitively settled, because the difference is cultural, not technical, and cultural attitudes change with time and location.

Personally, the technical-ish definition that makes the most sense to me is "if it's a competition and people are gathering to watch it without participating, then it's a sport".