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There is nothing that would prevent them from establishing their own non-profit entity as long as they can prove that they are not a for profit enterprise to the IRS. The section you are referring to is about "clubs" in CA and while they wouldn't qualify as a "club" under that definition, they could still have their own non-profit. Clubs generally are seeking things like alcoholic beverage licenses and other types of licenses like charitable gaming licenses.
Under California law, a nonprofit board may be composed of as few as one director, but the IRS is unlikely to grant 501(c)(3) status to a nonprofit with only one director and most nonprofits have anywhere between three and 25 directors.
So they can start their own non-profit, it just couldn't be a legal "club" under CA law until they reach those requirements.