What is the role of sports in promoting World peace? considering the olympics and other competitive sports.

I don't disagree with the answer above, but let me play devil's advocate just so you have another point of view to consider.

With the Olympics, we are talking about world-inclusive set of athletic contests that happen every two years, winter and summer games alternating.  Every country can participate if they wish.  Every country is validated in opening and closing ceremonies.  They are broadcast worldwide, watched by billions of people, and are a set of contests resolved by peaceful competition.  While this doesn't directly cause all countries to be at peace, it is a peaceful event, a positive event, an egalitarian (based on equal opportunity) event, and certainly creates an atmosphere for peaceful relations.  During the Cold War, it was one of the few ways in which Americans and Soviets interacted.

With World Cup soccer matches, this is a huge event in many countries, and growing in popularity in the United States.  While many of the fans themselves have been violent at times, most of that is based on alcohol rather than true tendencies towards violence, with some notable exceptions.  I think anytime countries come together to compete, it is overall a positive experience.