What’s the issue with providing KYC, what are you hiding.
There must be 4 or 5 exchanges that have my full KYC, bank statements, selfie photo, home address, mobile number. I don’t understand your problem, if you need to provide KYC to withdraw funds then do it.
Many people do not want to do KYC because:
1. They might have not necessary documents
2. They think personal information might be compromised
3. using multiple accounts
4. Mislead something etc.
But for this user I think nothing happen just lost on bet and behaving like a child.
I also do not like KYC but if a situation is like this similar to OP and showing the KYC can be beneficial to get the funds back, its better to do the KYC. That's why most of the gambling site does not require KYC, but in case of any issue or despute they can demand the KYC.