It's hard not to see this as Apple looking a gift horse in the mouth, while the barn door was left open months ago for it to run out and propagate itself across every farm in the land. Apple could have voiced this concern about the Google Chrome Web App Store, the Verizon VCast App Store, the Nokia App Store, or others.
Intel has an app store, Samsung, Motorola and LG have app stores. My local public transit agency in Portland, Oregon has an app store. I bet you can think of some more app stores, too. Google News can find more than 6,000 news stories that used the word App Store in 2010 alone - excluding stories that include any words associated with Apple products!
Sure, many of those are unofficial names - but everybody knows now what an app store is and just about everyone knows what The App Store is, too. Apple's being one of the very largest companies in the world and continuing to make products that millions of people love both seem likely to be more effective in protecting against brand dilution than trying to get other companies to stop calling other things App Stores now!
An app is an application, a discrete piece of software. A store is a place you can buy things. An app store is a store where you can buy apps. I must confess, I haven't looked closely at the reports about the Amazon App store yet. This sure makes me want to, though.