Agreed. As far as I can tell the author's premise is: "normally the Gambler's Fallacy refers to things like coins and dice, where you don't know the precise odd

Agreed. As far as I can tell the author's premise is: "normally the Gambler's Fallacy refers to things like coins and dice, where you don't know the precise odds but you do know that trials are independent. But if we redefine it to refer to the opposite situation - where you somehow know the overall odds but you don't know whether trials are independent - then we find..."