If they are referring to TI's OMAP processors, then they typically feature multiple ARM cores with various media accelerators (http://www.ti.com/lit/ml/swpt034b/swpt034b.pdf). These are like all-in-one chips designed for mobile platforms that are optimized for displaying media on a LCD-ish display at minimum power. The OMAP offerings are pretty similar to chips from Broadcom or Samsung, however, it makes sense for them to get integrated with their biggest customer. They already have NDAs in place and TI probably has field engineers that essentially work for Amazon, they would just be transferring financial stake different production processes.
Having said that, the reason that you probably don't want to run a EC2 instance on an OMAP, or any ARM for that matter, is because they are not 64bit compatible, they do not have good virtualization support, and you would not be taking advantage of various media/display capability.
Is there anything inherently wrong with ARM servers that give you legitimate reason to immediately balk at the suggestion? As far as I can tell, ARM servers are no less reliable or speedy as x86 servers. They just cost less to own and run. In fact, there's already a sizable precedence of ARM server clusters like EC2 (and including EC2). See:
Yes this argument is becoming true with time because ARM is really gaining phase. But we have Virtualization and its already cheap and works best at the moment. I dont see why anyone should go for separate ARM server ( in normal scenarios of course ) instead of using virtualization
Has anyone considered that this could also be for ARM-based servers instead of just Kindles? :-)