A customer has had a history for the past 2 years with a merchant (online gaming) and no suddenly wants to dispute recent charges claiming they are unauthorized because they overdrew the account. What is the customer liability? Would Reg E still apply? What are the Bank's options?

Yes- Reg E applies- you have a customer asserting an unauthorized charge.

You could simply credit the customer, or you could investigate to see if you can determine whether or not the new charges are associated with the same gaming account as the historic charges. It depends on how much money is on the table, and how far you want to push the matter.

In either case, I suggest that you consider cutting off the customer's card privileges, and possibly even close the account.

A pattern of doing business with them, and now, because the account's overdrawn, there's a claim that recent activity wasn't authorized? I'd be falling back on the customer's pattern and practice, denying the claim, based on his account history.