If you are running after a bus are you doing a sport ?
If you are a boy racer and love speeding in your automobile regularly are you motor racing ?
If you get shitfaced and jump around on a nightclub floor are you competition dancing ?
Being physically fit doesn't mean the activity you are doing is a sport, people who go to gyms to work out and run on treadmills and lift weights, they aren't considered to be doing a sport
Climbing is WAY more than a sport