The board didn't rule on the core issue of whether players are employees. Instead, it said that allowing players in private schools to unionize would lead to a competitive imbalance because players at public schools might not be able to unionize. By refusing to take jurisdiction over the matter, the NLRB refused to certify the union, thus rendering the vote by players meaningless.
http://apps.nlrb.gov/link/document.aspx/09031d4581d7160d