“"Because Dartmouth has the right to control the work performed by the Dartmouth men's basketball team, and the players perform that work in exchange for compensation, I find that the petitioned-for basketball players are employees within the meaning of the (National Labor Relations) Act," NLRB Regional Director Laura Sacks wrote.”(underlining mine)
So the test is apparently whether the university can control the “work” (practices and games presumably) performed, and the players receive compensation. Clubs wouldn’t seem to meet eitner criteria. (but I am scratching my head over what compensation the non-scholarship Ivy League players are receiving, since I thought colleges couldn’t directly pay kids)