Right but I wouldn't say it's of zero economic value. I think when people play music or sports, they're acting as both the consumer and the producer, and the analysis of economic surplus can proceed as usual. They produce and consume up to a quantity of music/sports until their private marginal benefit equals their private marginal cost. The total surplus is the integral over the marginal benefits minus the marginal costs.

The difference between an amateur and a professional is that the professional's playing adds marginal benefit not just to themselves, but also to others who watch/listen. They are then compensated in the market for that production.