K.P.
He learned that it is about winning and not about fun from somewhere. A coach, other kids, or yes even his parents. Kids learn this by the cues they are given. If they are always cheered "Yeah you won" or "great hit" but never told "wow that was fun!!" even if they didn't win thats what they learn. This starts from an early age, when playing simple games like candy land, and catch. If all they here is cheers for winning or doing well they think that its all thats important.
You stated that they play a few sports. Maybe sports are too big a focus right now. How old are they? Are they involved in a variety of things for their age? Also, do you go to practices and watch how the coaches and other players interact with him. This may give you a clue as to where he is getting this from. If a coach is giving him this message that is a major influence on his perception in this realm.
Sit down with him. Tell him that you want him to play sports because you want him to have FUN!! Tell him it makes you sad when he gets so upset and frustrated. Ask him "Why does it make you so frustrated when you don't win?" Get his perspective. You might learn some interesting things from him. Don't be afraid to talk to him and find out his thoughts about it too. Then tell him you want him to learn to just ENJOY it! He's a kid--he shouldn't worry about winning......then help him do that.