Competition -- whether in sports, academics, or the arts -- can show any person how to deal with both success and defeat. This is a valuable life skill, and the sooner it's learned, the better. I have seen cases where gifted kids go off to college and basically fall apart academically when they see that there are many high achievers like themselves.
Competitive activities do not have to be so expensive, stressful, or time-consuming that they disrupt all family life. Competition can take place at a local softball field, or at a local Scrabble game club. School competitions are also good: essay contests, math games, etc.
As parents, we can let our kids know that all they have to do is make a good effort and that's what counts the most. Talk with them about what they got out of the competition, whether they win or lose. Let them know that quitting in midstream or having temper outbursts in public are not acceptable behaviors in your family. For a gifted child, competition in areas of their interests can also help them to meet other kids who just might become friends. This can be a win-win situation for gifted kids! Good luck.