I'm not arguing this gives Apple any legal ground at all (it's not a case I'd like them to win), but I think their role in changing our use of the word "app" to mean "smartphone program," and increasingly only "smartphone program," shouldn't be ignored.
The case is a bit different than your example, because they branded a subset of the application market (perhaps the original "app") as "app," a subset that previously hadn't been very profitable or popular. For example, if I decided to sell an emerging, but not original coffee product as "java," (bad example, I know) and called my marketplace "The Java Store," if another company, seeing my success, decided to create its own "Java Store" that sold the special kind of coffee product I had been selling, it would be painfully obvious they were trying to ride my coattails because I, through painstakingly precious and irritating marketing, built the associations between "Java" and some silly little coffee product, instead of coffee at large. The fact that some competitors may have tried to use "Java" to describe their somewhat different coffee products (i.e., Google and "Google Apps") but failed to brand that connection in our collective lexicons, to some extent demonstrates that my marketing was special (because it turns out Apple is "cooler" than Google) and I deserve credit for that.
But again, I don't think that should have a legal basis, but I think we all do know that Apple has changed how we can use the word "app," at least for the time being. If you tell your boss "I'm thinking of developing an app for brewing coffee" s/he is going to think "new $0.99 (I have no idea how much they cost) smart phone program," not "big Windows application." At least that's my hunch. Especially for the kind of people who will make most use of this new "app store."