Hi Tigerle. Sorry you and DS are having a tough time. It does sound as though it is more than just sporting prowess causing distress but maybe that is one way for him to articulate that life isn't going how he would like it right now. Sounds like he may be having some hassles and being picked on? Is it possible that being teased for being good academically has morphed into, if I was good at sports I wouldn't be a target for teasing?
You have had some great advice and I think many of us sympathise from personal experience that not everyone is athletic. My DD has major hypermobility issues and has dislocated various joints trying to be a participant in sport. Like your DS she likes to ski, although we have to be careful with it now we know the extent of her Hypermobility. She attends a physiotherapist who runs classes for hypermobile kids once a week. The classes are part physio, part pilates, part yoga. Some of the kids are sporty despite their hypermobility and are working to build up their strength and protect joints. Our DD does special exercises before we go skiing for the same reason.
Is there a Physiotherapist involved in your DS's care who could help? Can you use skiing as a reason to do exercise and improve strength and fitness so he enjoys it more when winter rolls around? That way he is "in training" and doing a sport but it's his sport's off season!
I would also look a bit more closely at why he thinks he has to be good at a sport. Maybe in a calm moment he might tell you more about what is troubling him and you can address any other issues. Stay firm with the Internet boundaries. They are always a challenge! And good luck.