I hardly doubt that exchanges would ban transactions to gambling sites since they aren't even government-controlled in the first place, why would they even care.
I see it exactly the same way, why should they? The exchange is not responsible for where the user transfers their coins to, nor is transferring an amount to a gambling site illegal. So I am 100% sure that this is a misunderstanding.
What I could well imagine though is that the exchange does not allow withdrawals to old BTC addresses and only allows segwit addresses for example. However, some gambling sites still use old BTC addresses.
Without an exact information of the support why the withdrawal was held back we will not find a solution here and can only speculate.