Don't fight the neurons
Here's the problem with the term "Desktop Website". It's an oxymoron!
From an end-user's point of view, if something is on their desktop, it is not on the web. Their desktop isn't on the web, their other applications aren't on the web. If they use it locally on their machine, it's an Application or a Program.
Yahoo! is a website, because it's on the web.
Radio is not a website, because it's on your desktop. Radio is an application. It's a little weird, because you use it from your browser, which is where other web things are accessed, so it's a web application. But it's not on the web, so it's actually a desktop application But wait, it's not like your other desktop applications like Word and WinAmp, it's run in a web browser, so it's a Desktop Web Application.
There is a distinct different from a Desktop Web Application, and "running a website" or "having a web server" on your local machine. Applications are programs that run on your machine, and servers are things that vend content to other people.
In fact, Radio even makes this distinction! There are two sides to Radio... it's Desktop Web Application server, and its Web Server.
The Desktop Web Application runs on port 5535.
The Web Server runs on port 80*.
(*or 8080, if your OS' Personal Web Sharing is already running on port 80)
I say, don't fight the neurons of the people who have 20 years of experience running desktop applications and 10 years experience accesing websites. Keep the terminology distinct and clear, and everyone will understand what it is.