All games are not sports. A certain physical prowess and skill is a requirement for me to think of an activity as a sport, in addition to some direct competition. Everything else is just games, hobbies or just plain ol' competitions. Moving a mouse or laying cards on a table do not qualify. American Idol is not a sport.
American Idol is a competition, not a game. It's not an activity governed by a set of rules or customs (you just do what the producer says and if the audience likes you, you go on to the next stage). It's not particularly competitive, you just do your part and see what happens.
Skill is not always physical. Poker takes a lot of skill to master. And it is physical if you're fat.
And, have you never gone to school? I'm sorry for being pendantic, but I was pointing out how that loose definition of sport encompasses pretty much everything.
If you're pendantic, yes. The term covers any competitive game that requires a level of skill to play, in my opinion.