I believe this is being followed for the purpose of making everything transparent and not to get into illegal things. If thats the case then these exchanges shouldn't accept funds from gambling sites.
You have a point, that particular exchange doesn't want to make it appear that they are supporting that gambling site by letting you transfer to that gambling site, if they have nothing to do with the gambling site they should clearly state it in their TOS that they are not accepting or allow withdrawal for a gambling site addresses, it appears they want money to get deposited only at whatever source.
Exchanges are trying to regulate gambling activities as much as possible and you just got unlucky because you’re dealing with the exchange that prohibit that activity since we all know, gambling is one of the place to spend fraud money and they are aware of that. The good thing here is that, they didn’t freeze your account easily and get coordinated right away, maybe its better to stay away from that site for now especially with regards to gambling.