Let's make it pretty simple. As BC game support already replied and agreed to cooperate, then it would be solved shortly. We need just two things to verify your transaction. You need to add your wallet dashboard screenshots, which address the BC game provided to your account. And transaction ID that you sent funds to the same address. This two pieces of evidence would help to resolve the issues.

It seems you provided screenshots from the exchange that you withdrew funds from. So please add the BC game address screenshot and transaction ID. So we can check on-chain where the funds are right now. BC game support seems supportive in your case. Don't make it complicated by just replying with content without evidence that I asked.