Distinguishing between intrinsic and extrinsic competition may be a key to avoiding the soul-crushing effects of highly competitive sports and finding ways for people to enjoy physical activity for "its own sake."
"Do you play sports to win or just for fun?" This is a question sports lovers often have to suffer. A sensible answer is "Both". Why see them as opposites? Well, obviously, because people who are really keen on winning often seem to miss out on having fun. Doing sports or playing games only to win seems like a lot of work. Yet, all sports lovers know that the real fun lies in investing yourself 100% in the game, and that means--quite often--going for the win.
To be more clear, let's make a distinction between the activity and the points assigned. Consider basketball. Dropping the ball into the basket and receiving two or three points for that are two very different things. In soccer, scoring a goal and scoring the point allotted for that goal are two different things. Some basketball games with kids are played without anyone keeping the score, to help players and parents focus on the fun of the game and forget about which team "won".
Now, to name these two different aspects of the game: In badminton, the energy expended to win a rally--the running, jumping, smashing, clearing, dropping, rushing, all the magic you try to do with the shuttlecock--is the intrinsic aspect of the game, the fun and exciting part.
Obtaining the point that goes with winning the rally is an extrinsic aspect, often associated with pride, glee, ego-involvement, self-esteem, etc. Points accumulate into sets, games, matches, tournaments, championships, medals, club chauvinism, patriotism, olympic honor--a huge grab bag of extrinsic reasons for doing sports.
In some sports, like most ball games, the challenges to be overcome by the athlete is provided by the opponent. This is how the game was designed. In order to have any fun running around trying to hit a ball, you have to focus on beating your opponents. This is where intrinsic and extrinsic motivational factors become intertwined and hard to disentangle. Beating my opponent and having fun seems to be the same thing.
But they are not, as testified by careful analysis. Struggling like crazy to win a rally or move the football into the end zone is absolutely possible without regard for the score, the recording, the tally. Because what if no one keeps the score? Easy in basketball, harder in soccer, but the principle is clear: You can have tremendous fun trying to outscore your opponent without actually keeping the score (although the English language doesn't help: scoring a goal means both "moving the ball in between the goal posts" and "obtaining the tally point assigned to each ball that was moved in between the goal posts." But the former is intrinsic motivation, the latter extrinsic.)
Other physical activity, like recreational downhill skiing, does not involve beating an opponent. The material context provides the challenges: the slope, snow, moguls, obstacles, visibility. We seek out the conditions that will give us the optimal challenge: Not too easy, not too hard. And people usually don't score each other at the end of run ("Hey, I did it in two minutes and eleven seconds! You?"), because that defeats the purpose of seeking out the suitably challenging parts of the course. That sort of skiing is entirely intrinsic, hence often a vacation activity. Competitive skiing is different: Opponents must be beaten.
Why is this distinction important? Because many of the negative aspects of sports, games and physical exercise are associated with extrinsic competition. People cheat in sports when points are important; fair play becomes a fool's game. Doping is rampant in elite sports, with the known health risks. All players know the unwelcome nervousness before an "important" game. Many athletes suffer from anxiety and depression and eating disorders. Betting, gambling and ludomania in the context of sports would not exist if no score were kept. Soccer hooliganism is all about winning games and championships. The Romans knew how to use gladiator games to keep a disaffected populace from rebelling: panes et circences, "Keep them happy with bread and circuses." American Super Bowl hysteria may equally seem an orchestrated distraction from the mounting economic inequalities of the 1%-takes-all economy.