This issue hasn't been explained properly in *any* of the articles I've read about it. I had to go to Amazon to find out what's actually happening.
If your account had a record of buying a Kindle e-ink reader, then there was the possibility that you didn't have wi-fi or cellular access. So how do you load books onto the device? They allowed you to download the encrypted book to a computer, so you could then load it onto the device via USB.
The encryption was designed for that specific device, so if you had multiple readers you had to download it multiple times.
IMPORTANT:
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If You Didn't Have A Record Of Owning A Kindle Device, Amazon NEVER Let You Download The Books.
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"No compatible device found"
How can you read them without a Kindle device? An app on another device, e.g. phone, tablet or computer. It's what I've always done.
Of course, once you download the file, cracking the encryption is a possibility, though of varying degrees of illegality depending on your specific jurisdiction.
I do wonder what the people shouting about this were actually doing with the files, which they won't be able to do now. I presume they all had a device but no other method to transfer books, which is now useless. This wasn't a campaign to drum up views and clicks via feigned outrage, oh no...