I like this definition.
My definition is that it has to be both an athletic competition AND a game. You can have athletic events, such as ones that I participate in (skiing, cycling, running, swimming, ect), but they are not sports IMO because they are not a game; just an athletic competition. And then you can have games that are not athletic events, and thus they too are not sports, such as Poker.
Why the need to limit it to a 'game'?? Skiing, swimming, etc., done competively are sports.
When we participate in them, for exercise or whatever reason, it's an activity. When world-class athletes compete against each other in these same activities, it's a sport.