by law any prize money over $600 in total from the contest should be recorded and that organization has a legal obligation to file a 1099 with the IRS. To do this they need a W9 that lists your SSN/EIN (not sure what the TIN is).
Ahh, that makes sense. Yes, if there is prize money involved, you will need to give them a W-9. However, you should only have to do that if you actually win money. If you finish in 25th place, and there is no money paid out, then technically, there is no need for a W-9.
If you are really nervous about giving them a W-9 with your SS number on it, see if you can defer it to when, or if, you win something.
Otherwise, if you believe the competition organizers are ethical and professional, just fill it out and submit it.
CD