I believe they have the capacity to trace the transactions, for an exchange, I guess it's easy to know if the wallet belongs to the exchange or to a gambling site. So if both are registered, then there's no problem with tracing, and the problem only is on the users who violated the rules of using the platform.
It's easier if both businesses are registered as they can easily track down
all the transactions and sort which are those who violated their rules.
Easy for these companies as they need to comply with the government to avoid having problem with their business permits.
Direct withdrawal from point A to point B is already risky, that's why mixers exists because they will help to hide the real origin of transactions.
Mixers is the best option if you don't want to track any transactions that you need to take,
more safer than trying your luck not to be detected.