Except for how "app" isn't the one word used by everyone to describe the thing sold at the App Store. Software for computing devices is generic, and "software store" is certainly as generic as "shoe store". Apple wasn't the first to use the term "app", but they certainly were the ones to popularize it, and most certainly for mobile devices.
Prior to Apple's "App Store" you could download software for your mobile device -- your Palm PDA or phone, your Symbian PDA or phone, your Microsoft Pocket PC PDA or phone, your Nokia phone -- from a wide range of "stores" and, strangely, none of them were called "app store". They weren't even called things like "Palm App Store" or "Pocket PC App Store". If it's so obvious and generic, why wasn't it used? Why weren't those software downloads even called "apps"?
If Apple had decided to call downloadable software for the iPhone "applets" and opened the "Applet Store" and everyone who followed started calling them "applets" too and opening up "applet stores", I take it you would similarly argue that Apple's trademark on "Applet Store" would be invalid because suddenly everyone's using the term "applet", is that right?
What's the reason that downloadable software for a mobile device has to be called "apps" by Google or by anyone but Apple?
I'm playing a bit of devil's advocate here, in that I suspect the trademark won't end up being defensible, but I strongly feel that the "it's a completely obvious use" argument simply doesn't hold water: if it was so obvious then it would have been in use, and if "app" was such an obvious generic term for downloadable mobile software then they would have been called "apps".