if any entity requests KYC in order to continue using their services they should at the very least allow those customers that do not want to continue being their customer the opportunity to withdraw their funds before closing the account. I am unsure how BC Game operate in this respect therefore maybe someone more informative will address this.
Unfortunately, this is not how things work. According to my experience the moment a casino or any other service provider asks you to verify your identity you will no longer be able to withdraw your funds until you submit your documents and successfully pass the kyc process. Some of those service providers will let you continue use their service in the meantime.
According to factor280's experience, it seems bc follow the same procedure.