If you are not seeing the updates…
From your account page, along the top menu look for “Kindle Support” and click on that and then click on “Contact Us”
Wend you way through the questions answering things like
Select an Issue: Kindle eBooks
Select issue details: Kindle E-reader
Select additional details: Something else
Box 3 will give the option to contact them via phone or chat.
Explain your problem, give them the ASIN of the book: B01N6DL30K
Tell them the author has updated the book and you want the updates, they should push them to you.
If your issue is with the Kindle Cloud Reader, tell them it doesn’t work (assuming it doesn’t) and that the author has personally told you that it should work and that it is a problem on the Amazon side.