Ask the kid that got to only play one quarter in Little Dribblers if he cares who won or lost. Ask your kid if he had the following option, which one would he prefer:
1) Win but only get to play 1 inning
2) Play the whole game as pitcher and/or shortstop
Most kids choose the option to play as opposed to winning. Everybody wants to win but in the end, they care more about the experience than the won/loss record, ESPECIALLY when they are 7 & 8. There's plenty of time for them to learn about winning and losing.
I've coached somewhere around 30 teams in baseball, softball, and basketball. Kids want to play, have fun, be with their friends, develop skills, hit the ball/score a basket. Winning is not real high on their list of things they want to accomplish.
Now when they get to high school, I'm with you. It's all about winning.