Hmmm ... I guess I'm not the general public, but I'm running a fairly generic install of Firefox 2.0, and the page comes up with a big grey box with a red X in it. I'm not actually sure why this is, as I'm sure I've had some Java apps working in the past.
Update: Oh, the Java console shows something about an "UnsupportedClassVersionError".
That happens when you try to run a Java app that was compiled with a newer compiler on an older VM. Most likely, the demo was built with Java 1.6 and you've still got 1.5. It's working on my browser.
...It's also slow to load and incredibly clunky. Why, Swing, did you have to reimplement every native widget so that none of them look the way we expect? I think Paul's "no Java applets" remark is on the money here.
Update: Oh, the Java console shows something about an "UnsupportedClassVersionError".