Even the first definition in Webster's is "of, relating to, or affecting all or most of the people of a country, state, etc"<quoted text>
He's trolling. He did not ask for a legal definition. He knows he is not using terms correctly.
He posted a Webster's dictionary definition of "public" and then tried to argue that that takes precedence in discussing this issue over the legal definition of "place of public accommodations."
Don't post as though you're explaining the nature of the dispute to him. The troll not only understands that, he purposefully generated it.
Trying to make the case that public = of the state in this or all contexts seems like a hard row to hoe.