If I ask for a customer to produce ID to verify their age, and they "don't have it," I inform them that they can not be in the casino without ID. Inevitably, I get hit with "What law says that?" I typically respond, "this is a privately owned establishment. It is our policy to require that every patron have a photo ID recognized by the United States in their immediate possession at all times while on the casino floor."
In the club I work at, we do not accept identification issued by a foreign government. People always throw a hissy fit when we tell them we do not accept Mexican, Canadian, or other drivers licenses. "Not to worry," I tell them, "The US State Department clears all passports issued by other countries, we will gladly accept it as a form of ID." and then I have to listen to them cry about how it's in their room at Hotel X, Y or Z. Then I have to go into how we can not possibly know how to identify every ID and drivers license from every country in the world, but Passports we can train our staff to verify and since you must have a passport to enter the US, we know you have one!
Just like casinos can ask you to leave for doing something that is not unlawful, such as carrying a firearm, they can also require you to carry ID and produce it on demand. whether it is written into law matters not. I will say that it is inappropriate for people to disguise a company policy as law, they should just say "Sorry sir, company policy."