I don't think Apple will win this one. Apple is in the same position Bayer was in with the trademark of Aspirin. Aspirin used to be a product until everyone started using the word to describe "Headache Medicine". The word "App" has become synonymous to mobile software. The word is now an identifier of an object, and therefore having an "App" Store, is the same as saying Old Navy "Clothing" Store, or such. App Store is a store that sells Mobile Software.