This actually depends on who is interpreting the signs. I have had lawyers tell me that the signs do contain force of law and not other notice need be given. Much like a no smoking sign or a no shirt no service sign. However, given that information, the city of Moore Police Department requires the owner or manager to give a verbal request before they can charge a person with trespass. The sign at Chuck-E-Cheese specifically states the sign serves as your notice.
Chuck-E-Cheese doesn't have a clue and you need to talk to some more knowledgable attorneys. Any area not specifically prohibited by statute is not "illegal" to carry in. That's what statutes are for.