This sounds like the tips & tricks you see in Pagespeed/Yslow, moving it to a proxy, coupling it with something like SPDY, and mixing in some server side caching. Which is neat, and no doubt will achieve some speedups. But I don't know if it is as revolutionary as Amazon is trying to make it sound.
There are also some serious privacy implications here. I don't really know if I want Amazon to cache & potentially record all my browsing, especially since that device is something they can directly connect to all my personal info (purchasing history, CC number, home address, etc..).