Very interesting. However, what I was referring to was that Apple was the first company who launched a marketplace for native software programs, a marketplace carrying the name 'App Store', AND which was integrated in the OS. When we speak of 'the App Store', it's obvious whose marketplace we're referring to, even though other companies have launched similar software marketplaces for their own ecosystems (Google, Microsoft, Amazon, Canonical, etc.)
That's not to say that the separate components of Apple's App Store were particularly novel. Before its launch, there were package managers, there were online marketplaces for software, and the name 'app' had already been used by several platforms. Apple united those ideas, made it a user friendly environment, made it easy to buy apps with one click (using the credit card that was already on file in iTMS), and integrated the update process. That's often how Apple gets their successes, by combining and improving on existing ideas (see OS X, iPod, iPhone, iPad, etc.)
I never used Acorn's Archimedes, but growing up in The Netherlands, the first computers I used were Acorn Electrons, our primary school classroom had six of them. That's how I started programming, in BASIC, at the tender age of 6. I have fond memories of using those machines.
http://en.wikipedia.org/wiki/Acorn_Electron