And you need to think about why your DS spends his free time on the PC. DSS2 has strong inclinations that way, and it is because he is shattered most of the time and cannot manage more than TV/computer/handheld console while lounging on the sofa.
By 12 I think they ought to choose their own activities. My dd is 13 and very busy but that's how she likes it. I keep on suggesting she drops an activity, but she doesn't want to, and while she's fitting in the homework I'm letting her get on with it.
I do insist on most Sundays being quiet at home days, though.
I would let him drop what he wants to drop and take up gym.
Is there anything so terribly wrong with spending an evening on the PC? It does sound like he's doing an awful lot- - if he's not actually keen on these activities, then what are you teaching him about choosing how to spend his time? Just that being busy is "good for you"?
Children do need some wind-down time, same as the rest of us. Yes there are some adults who want to be active every waking moment, but they are the exception not the norm.
I would let him swap one of the activities for gym, if that's something he wants to do instead.