That could happen reminds that regulator/government can ask that to the casino because casino can check to all of their members. So when the gamblers win much money, they must pay the tax to casino and the casino will report and gives the tax to the government. The gamblers can only obey the rules from the casino so they don't have to pay the tax to the government because their winning deducted to pay the tax. Everything can be possible as the government have the power to control the casino under them.
It is true that the casino can check all of their members and they do that too for security purposes. But while it is a matter of tax I think gambling sites should bear the tax of their end which they earn only. And for the users, the users are liable to their country whether they will pay or not.