Other casino usually solve this issue without fee since they will just need to import the wallet private to wallet that support the network of the coin. I understand that they might charge some fee since this is an extra work but they can use this opportunity as marketing by solving the issue without any fee to boost their reputation now that they are strengthening their reputation here after they solved all their pending issue last year.
I’ve done this mistakes twice on 2 different casino which I will not name and all of them solved it within 24hrs without any fee charge from me.
I don't have experience with losing big money by sending it to a casino that does not support that chain or token so I can not say about casinos and how they resolves such serious mistake and big loss for their users.
Usually on centralized exchanges, they will not automatically support their users for such troubles. They have notification, reminder that users must check blockchain, token support and address very carefully before finalize a deposit or withdrawal.
They also have terms that in case they support users, they will charge support fee and as I know, fee is not cheap.
Support without any fee, like you shared, I did not know about it, never read it anywhere.