It's a game. It's UI is full screen and completely divorced from "standard" UI elements (WIMP, etc).
You can call it a desktop app, and you'd be correct in the most pedantic sense, but then every web app is also a desktop app since you run it on a desktop.
Still, not really in the sense of the article - he's talking about desktop apps like word processors or email clients: Minecraft's GUI is just a big canvas that the 3D renderer renders into. It's not using any windowing components - IIRC, even the menu and buttons were custom.