That doesn't sound any different than most similar electronic devices. No one ever advertises that the online services will be available forever, I doubt Amazon advertised they would work or be supported forever.
For a real world example that's nearly identical... any Internet connected video game console that are now End of Life? The Nintendo eShop is no longer available on the 3DS and Wii U for instance.
As far as I can see, these Kindles still work with whatever they had loaded on them at the time, they just can't connect and download new files from Amazon's services. They still let you side load files directly on the devices. And you can always jailbreak it.
None of those options are any different than what is available on the 3DS and Wii U now.
core functionality—that is, continued access to digital content on the Kindle Store—
I would argue, and Amazon almost certainly will as well, that the core functionality is viewing books. Which they can still do just fine.