I cite Thefreedictionary not as an authority I'd need to rely on in court, but to explain the principle of a unilateral contract to those who may be unfamiliar with it. A US lawyer and US court would be familiar already! One wouldn't need to cite a definition of unilateral contract. Perhaps some caselaw, but even that is superfluous.

It is true that a contract requires offer and acceptance. But the form of the offer and the form of the acceptance may not always be signed instruments that lay persons would recognize as "contracts." In a unilateral contract context, the offer is stated to the general public, often as general as an advertisement. Then acceptance is via an act (e.g. buying a product). Publishing a web page of policies and benefits can be a unilateral contract offer. Buying a business class ticket ($$$$) and arriving at a lounge is a proper acceptance of such an offer.

BA is subject to US DOT regulation and to breach of contract claims in US court. This is well established in myriad proceedings including multiple US DOT actions against BA for all manner of violations, as well as multiple consumer claims against BA in US courts. I could post some citations if you like.