People participating in competition and winning (or not) are in my opinion self driven individuals that are more suited to build their own company as opposed to be a good employee.
"Here are the exact specifications of the format of input and output into a console application, and the exact specifications of how the output must relate to the input. You have one hour to do this and your program must finish running within X seconds of being invoked on our test input."
I can't see how being talented at this would have any connection to talent at building a company, in fact I wouldn't be surprised if it was negatively correlated. I'm not really sure talent at winning programming competitions could be positively linked to other than talent at winning programming competitions. Valuable industry tasks differ substantially from what is done in a programming competition.
I agree, if you consider such question I don't see any relation either. What I meant was a general competition (not strictly programming). If you participate, it means that you want to achieve something, hence self motivation. Of course self motivated employees are great for the company, no doubt about it. But I feel that too much of it may conflict with the interest of the company.
The hard part of really building something is keeping to it over long periods of time, though. That seems quite different from being up for a competition.