The American Consulate has confirmed that competitors who are eligible for the visa waiver programme will not need visas. See extract of confirmation below:
You indicate that athletes will participate as amateurs and receive no prize money, only medals. Travel for this purpose is permitted under the Visa Waiver Program. Therefore, athletes who are eligible for the Visa Waiver Program will not need visas.
Details on the Visa Waiver Program are on our web page at: http://www.usembassy.org.nz/nzservices/visas/
You may also contact the call center for visa information at the toll number 0900-USVISA.