I don't recommend the book but this link on amazon allows you to "look inside" and see the author's opinion on the definition of what he considers a game compared to a puzzle in the first chapter.
(Spoilers) In trying to put everything in a neat little box of labels he considers a contest a type of puzzle, and a game a type of contest, which does fit with the OA quote.
It's a small print run right now, and I (obviously) don't have the money to do a book tour, but I am talking to the publisher (CRC Press) about other ways to promote the book. Here's the amazon link, I think it becomes available in just a few hours.