could you detail the difference between sports and exercise? running is a sport and it always seems to me that there are a lot more women out there jogging, not to say participating in races. is the competition issue your focus?
Exercise means non-competitive. For example, if you work out on a stairmaster or do a yoga class, you wouldn't come home from the gym and tell your friend that you "won." But you might do this after playing pick-up basketball or soccer.
For the most part, though, we simply defined sports as those classified as sports in high school and in the NCAAs. (See the Methods of our paper for more details.)
Running was unusual, however, because it is a sport in high school and college, but we classified it as exercise. We did this because many studies of running participation confirm your observations that most runners have a primarily non-competitive orientation. My earlier research (and some ongoing research) indicates that of the small proportion of truly competitive runners, males outnumber females by roughly 3:1. If we had considered running to be a sport, the sex difference in individual sports would be smaller than we reported. But I think our classification was correct.
I hope this helps.