There will always be ways to detect users, and governments have all the tools at their disposal, especially those in positions of authority. They will certainly do whatever they believe will benefit them.
I agree with Dan, that if there were no KYC policy, I think casinos would also make it easier for their users to do so. They certainly know that most users are reluctant to undergo KYC. However, they must also continue operating, and one of the things they must do is implement this policy.
I do not think it will be that easy to detect, except for a suspicious financial cash flow from an account which would attract the government to it, but I believe gamblers are very smart and always know what to do to avoid the government's attention to them, except for those who are involved in financial embezzlement and are looking for ways and where to keep their money or conduit for which they would use to do their dirty deeds.
All these are the reasons why the government is hellbent on forcing the casino to abide by their policies, or they face sanctions, and the casinos too would not want to have any issues with the government and would also want to retain their spot, so they would abide by the government's terms and conditions to operate because they are a business venture too.
You might forget that the government has everything at its disposal; they have all the tools needed to track anyone, including any transactions they make. Any company operating under the government's jurisdiction will certainly provide information, especially if they say something related to security.
They might even be playing a role. This means that even when a country prohibits any gambling activity, there are still individuals who facilitate it because they profit from it. This is nothing new and is common knowledge, and it's not limited to this space, but it's prevalent in all areas.