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The no-KYC part from crypto games was one of the biggest selling point in the beginning and the reason a lot of people joined them also. Personally, I don't have an issue with doing it as long as it is a reputable casino that has proven themself over 1-2 years. A license helps for the credibility, but is also no holy grail.
Personally, I also have little problem with performing KYC on a platform. However, it is important to me that KYC on a specific platform (e.g. BC.Game) does not also reveal my identity on another platform (e.g. Bitcointalk). For example, I do not use my account names and email addresses twice or use BTC addresses more than once for deposits/withdrawals.
Because you mentioned the license: Unfortunately, this has absolutely nothing to do with how secure your KYC data is and/or how trustworthy the platform is. Any of us could get a simple offshore gambling license in a relatively short time