That's a really weird experience, it's the first time I read that. But what I don't understand is how did they know the deposit address was belonging to a gambling site? Usually one address is at least generated for each account. So they have no way to guess that fresh address belongs to a gambling site. For me the issue was not related to the nature of the business of the recipient.
I'm not sure if most gambling sites still does this but I know a couple of sites like cloudbet sends all of the deposits they receive in their hot wallet and there are others that wait for the transactions to accumulate before they consolidate it as a way to save fees.
Instead, why not send it first from your clean wallet from a gambling site and then send it to the exchange platform that you have used. There will be an always solution for this if we really want to.
I guess OP wanted to save on the fees because last week there was a fee spike.