That's it, and gambling sites do understands that, even exchange like Binance which is one of the most popular exchange in the space is not so strict with KYC.
They allow traders to use their platform without KYC up to a certain limit or condition, because they see the possibility that they would loss clients if they will be very strict, same with gambling site of course, less complicated will give more comfort to gamblers and they will choose a gambling sites that gives them that comfort, people does not care much about the license of the gambling operators, they cares more on the reputation.
So actually, we as a trader and gamblers should not be worry if we don't want to do KYC because we can found easily the gambling website which does not require their members to do KYC. I guess that will help the gamblers to join in their site because the gamblers only want to play gambling without the want to fills the KYC. I think if the gambling site needs their member to fills KYC, they should get licenses from the gambling authority, and then they can apply the KYC to their members too. Besides that, the gambling website needs to fill KYC too like their members.