See, I'm not sure this is Apple-envy. Apps aren't particularly new, and although Apple were the first to really push them, they were there before that on the web too. Basically most web-applications (note: "web-applications", not "web-sites") are "apps". They're a bit richer than a page; not quite as rich as a full application. You visit there quickly to upload your receipts; to check on some stats; to read and compose email.
This trend was going on for ages before the phone came along. You want to write a tiny app that presents or collects basic data and processes it in the cloud? In 2003 the web was the app platform. When the iPhone came out, it became the second (or at least the second major, consumer) app-platform.
That's why web-developers found it so easy to go and write iPhone apps. The concept is the same. You take small amounts of data from the user or from sources around the web, process it "in the cloud" (we called it a website back then) and then show the data in a concise way with page-transitions, and voila, you have an app.
There's also the other type of app. You know. The one where the users have to click the ball and keep it up in the air, and there are these monsters that you have to shoot to get a good score - and those sprites slowly come towards you whilst you collect the gold coins in order to get three stars and a cheevo. You know. Those games. There are tons of those on the iPhone - but they started out life as flash games on the web - or, if you're historically minded, as arcade games in the 1980s.
Sure, the iPhone has both types of app - but let's not pretend that they invented apps. At best they maybe coined the name app - but that's not the same as inventing the concept in the first place. Website-y data orientated apps were on the web first, and the iPhone certainly didn't invent low quality games that cost a dollar to play.
This isn't a case of Windows copying Apple. It's a case of giving Windows what every other platform (other than perhaps Mac/Linux) already has. The web, Android, the iPhone, the Xbox, Windows Phone and hell - even the kindle fire, Blackberry and the Playbook all have apps that are glorified webpages and apps that are glorified arcade games that you pay a dollar to download, play for a week and delete.
The problem is that if you start with a Windows-centric viewpoint then yes. Apps are new and look a bit like iPhone apps. But if you look at the wider picture you see that Windows was the outlier. With Windows, the only way you could get your app-fix was to fire up your browser and go to the web.
The desktop had no means to fill this fix. You want a website-ish type of app? Well, you'll have to remember the URL or use the favorites bar in your browser, because otherwise you won't be able to find your app in your browser. And if the website wants to notify you of something you can either go overkill and use RSS or use a plugin to your browser (eugh) to get the notifications.
Want a game? Well, you can either play $30 for a multi-million dollar release game from hollywood that'll destroy your laptop's GPU and consume 10GB of space, or you can brave the EXEs on the internet and pray to God that it doesn't come bundled with something nasty that'll take your credit card details and send it to some Nigerian Prince in Eastern Europe. Or, of course, you can play a flash game - again, on the web.
WinRT isn't about "killing the desktop". It's about giving the Windows platform what customers have wanted for ages: glorified websites, and glorified flash games for $2 a time. The Desktop will still reign supreme for your big applications - your teir one games; your high-frequency trading applications; your applications bursting with functionality like Visual Studio and Office - for the foreseeable future.