The reason why they ask for a big size like this is because of the pixel density of some e-readers and they're probably looking for future device requirements. Indeed, it's huge and your print-ready cover file might not even be big enough to fit this requirement! So it's possible you can't even use the suggested requirement from Amazon for now.
But keep in mind that the numbers you quoted would be for the best quality on the biggest display with the highest density; it's a bit overkill since these numbers are even bigger than what e-readers can actually render. Not every e-reader needs it and you can simply lower these numbers down to fit the average e-readers. Of course if you can use the size you mentioned because your original design allows it, go for it.
And yes, the ratio is different from standard printed cover; the best is to create another version of your design for the Kindle cover. I think the ratio is actually to fit their last generation Kindle Fire e-reader, that's a suggested ratio, and it's different from most e-readers; you are still free to provide a wider one that may look better on thumbnail size.
It depends what you decide is the priority; that the thumbnail cover looks good in the catalog or that it fits better when viewed at 100%. As you guess, because of the different resolution of each e-reader display, you will never get a perfect fit on all of them at 100% unfortunately but you can simply decide to go with the average ratio most of them use.
A minimum of 625 pixels on the shortest side and 1000 pixels on the
For best quality, your image should be 2500 pixels on the longest side
So you can make your height at 2500 pixels, and if you want to keep the same ratio as you mentioned (1.6), your width should be something like 1567 pixels. That's more reasonable and it should be easier to adjust if your print-ready version was made for a 5x8" book.
If you want to fit the average e-reader, the minimum size could be around 1851 pixels width and 2500 pixels height (1.33 ratio.)