You are barking up the wrong tree. You are correct that Apple did not invent the term "App", but that has no bearing on the validity of the trademark.
"Open Happiness" is trademarked by Coca-Cola. Certainly no one claims that either word was invented by the company. PespiCo would be legally liable for using that phrase in an ad-campaign, however, a company in a different market (Dell for example) could probably use "Open Happiness" for computer sales without issue.
Are you familiar with "The Container Store". It's a store where you buy, wait for it, containers!! And yes, "The Container Store" is trademarked. No other company selling containers can use that name. Similarly, Apple was granted a trademark for "App Store". Just because App Stores have more competition than Container Stores at the moment does not make the trademark any less valid.