Not sure I would be worried about this if what you are saying is that this affiliate is ranking for other affiliate website’s domain names? There are like a billion affiliate sites on the web, I can’t imagine the domain names are remembered by many people searching around the web.
And how weak does a site have to be to not rank for their own domain name? Unless all the domains are simply using generic gambling terms for their domain. Still, you should rank first anyway for a search like “generic-casino-keyword.com”
Maybe I’m missing something, but can’t see how this is something to be very concerned with.