Whether "App Store" should be trademarkable or not is another question, but there's no doubt that the term "App" wasn't used at all before Apple's App Store.
Microsoft didn't even call Windows software "applications", they had always called them "programs".
I find it weird that a diminutive of a generic term is necessarily considered a generic term as well, even if nobody used the term. By the same logic, you couldn't have a trademark on something like "Mus Store" or "Boo Store". Meanwhile, it's OK for Microsoft to trademark terms like "Windows", "Office", "Word".
EDIT:
Okay, I did some research like macsmurf suggested.
Wikipedia:
In recent years, the term "app" has been used to exclusively refer to applications for mobile devices such as smartphones and tablets, referring to their smaller scope in relation to applications used by PCs.
There may be some anecdotal use of the term "app" before the iPhone (none of which I can easily find using Google, point me in the right direction if you can), but never was it a standard term used by any major tech company.
People started to refer to computer/mobile software as "apps" after Apple's App store, not before.
The only exception I can find is the term "Killer app", but like I said earlier, it has a different meaning. It's also the diminutive of "application", but you wouldn't use the term in the same context. For example, you could say that "X video game" is a console's "killer app". However, would you refer to console games as "apps"? I don't think anybody would, because it doesn't fit with the modern definition of "app" which Apple is responsible for.
Halo was the Xbox's killer app.
You wouldn't say "let's go to Gamestop preorder this app called Halo".
