The system is kind of working as intended? The publisher sent them a DMCA takedown notice, and since the site failed to take down the offending content, the publisher is fully within their rights to (1) contact the hosting provider and ask them to take down the entire site (2) contact the registrar and ask them to suspend the site (3) contact Google and request delisting of the site (the one department of Google that actually moves at a non-glacial pace) (4) take legal action against the John Doe behind the site and unmask them, maybe even garnishing their Amazon affiliate revenue.

The sooner you act, the better. But it seems like the publisher didn't bother with any of that, or they're just slow and are getting around to it. The author of the book couldn't even be bothered to respond to the blog author's question about it.