There are a lot of physical activities that do not have competition as a prime ingredient, the competition is mostly personalized. Rock climbing, or jogging come to mind. Are they sport? Or just exercise?
While [normally] requiring little physical activity, Poker and Chess and others, do require all the rest of the necessities to be good at any activity; practice, study, refinement and then performance.
Sort of boils down to ; Does the physical active of other sports mean Poker (or the other games) can not be considered a sport?
I can picture in my mind a thousand movies where a wager is proposed, and then some comment like "there's sporting fellow".
Maybe we need to come up with a more inclusive term for all competitions.