I happen to also be a competitive runner (ok relative terms and less so every year). I find my running to be very enjoyable but sometimes arduous at times as well (nagging injuries, not as desirous to run in snow and freezing weather as used to be).
However, I also play in a competitive men's league for basketball. Every year, new teams form with guys straight out of D3 colleges and high school teams. Our team regularly competes with only one guy who played college (D3) and everyone is in our 30s.
We play once a week most weeks. I shoot around about 30 minutes about once a week if I feel like it. I can get out of bed and make 9 of 10 free throws. Basketball is a cerebral game and I find I can play a pretty decent level off this "training." Making the right pass, reading the defense, setting screens, can be accomplished with no real time commitment, just an understanding of the game and playing as a unit.
If I commit to training I can run about my times in high school (slower mile, same 5k, better longer distances). Without any real commitment to basketball, I can play at a level at least as high as I played in HS due the nature of the game.
Note I admit being in shape is cab be an advantage in men's league and that my running contributes to some of my success there but most of it is feel for the game and hand-eye coordination that has not seemed to diminish much at all with time.