Well, you can exchange NGN for cryptocurrency not only on Binance P2pP, you can also do it on Bybit P2P there is also such an opportunity, it is safer and easier than a private exchange where you depend on the honesty of the buyer.
There many options available, i personally use Remitano, being using them since 2017, it is another convenient place to exchange naira to any other crypto currency and vice versa through the Swap feature or P2p, which ever the the user prefer.

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I think there is no way to make the transaction via Binance P2P also I do not think CryptopreneurBrainboss would be able to help the OP. As the site only accept Nigerian bank and if CryptopreneurBrainboss or others wants to help then that would be able to come true if they have the same bank account name as bc.game which might have not.
If this be the case, then its only the BC.game customer care that can help with solution on what to do, if OP still have this issue, then i suggest he contact the customer care of the casino, they are the only ones that can proffer real solutions at this point, if they still do not offer solution, then maybe they dont want the money withdrawn.