This is a very fact-sensitive question. Generally, an entity operates through officers and agents, not through its board. Although this may have been different, a board generally authorizes the President (or some other operating officer) to enter into a contract. The analysis of the "enforceability" of a contract starts with an analysis of whether there was a contract at all. Was there an offer, an acceptance, a "meeting of the minds?" Did the Chair actually enter into a contract with your friend or just tell your friend that he would be getting the deal? This is all going to be very difficult to sort out until the evidence of who said what to whom and when is nailed down. If the contract is valuable to your friend, he/she should get a lawyer would can sit down and go through the facts and match it up with the applicable state's laws on contracts AND organizational authority (including Bylaws).
First, you need to read the request for proposals. The RFP probably indicates what the selection process is and what the selection criteria are. A possible violation of bylaws would seem to be a good reason for the organization not to sign the contract.
Without a signed contract, there probably is no enforceable contract. There can be exceptions for partial performance based on a oral notice of award, followed by a notice to proceed.
I would have to review all the paperwork to provide a complete analysis. But based on what you have provided, I recommend that your friend not push the issue and make enemies. It may turn out that the other bidder backs out or is unable to complete the contract, and your friend can step in and save the day. If instead your friend antagonizes the organization, that will probably not happen.
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