Oh well, I never knew they had this condition mentioned on their site.
Although they don't have KYC for regular gambling on their site but this condition definitely means one can will need to do the KYC in certain situations.
I suggest that you understand the terms of service to know all the detailed explanations regarding the casino site used, but if you are an active user of the BC.games casino and have no problem with the limited gambling service features, then my assumption is that the casino site has not implemented 100% KYC for users or purposes KYC may be applied at any time according to the description of the terms of service.
In this case, I think there will only a few gambling sites which has no KYC process all together.
Even if you avoid casinos that have KYC requirements, you should consider safe and legal casinos, as KYC requirements must be applied following UKGC requirements to get a license to operate.