I was able to get the book by hitting the Oval-ish "Check Out with PayPal" button in the Shopping Cart. This opens a payment window with a choice to either pay with your PayPal account or enter your credit card details. The credit card transaction is then handled by PayPal, but you don't need an account. Only after doing this, and reviewing the order, can you enter the coupon code.
It's counter-intuitive, but there you have it.