If you don't have a mindset to win, then I personally don't see much point in playing.
Team sports can be slightly different, but I feel you still need the majority of players in your team to want to win, otherwise, you just don't go that extra step to push yourself, and that might be the difference between winning and losing.
No, I don't think that winning is the most important thing when it comes to sports. Obviously it is one of the primary goals, but I think that integrity is more important. In professional sports for instance winning by cheating salary caps, or getting away with cheating in the game itself invalidates the win.