bigger question here is not only KYC before deposit. What caught my attention is the combination of aggressive advertising, BLIK payments through unknown intermediaries, and the lack of clear information about who actually handles the money.
I have played at casinos where verification was only requested at withdrawal, but usually the operator and payment flow were much more transparent. If a casino is using third-party payment providers, I would expect it to be very clear who the merchant is and what company is receiving the funds.
For me the license issue would be the first thing to check before depositing. If there is no reliable licensing and dispute process, I would personally avoid putting money there, because problems usually appear only when you try to withdraw.