For anyone who debates this I would just throw out and say golf is in the Olympic Games which by definition would make it a sport.
I wonder how this question differs geographically / culturally. E.g. in UK I think golf is more “automatically” seen as a sport because there it’s a walking sport and there are not private clubs like in the US. I would argue the cart riding and private club factors is what gives golf the label it has in the US. Of course in years past it’s a fair comment that all tour pro’s didn’t exactly look like the poster children of fitness