The scenario that you linked to works for me. It seems that there must be some issue that is local to your PC. Unfortunately clearing the caches is the solution I know of.
Why should it not be able to find the class? When it doesn't work for you and then you clear your caches to make it work, what was the change that you did from not working to be working, that now it all of a sudden can find the class.
I do remember seeing the game before (I seem to remember it downloaded but I don't think that's possible if the gfar was never uploaded), but that was a long while ago, ever since that one time, it hasn't worked. I remember that there are different battle field layouts with hills and valleys. There is this blue person who gets controlled by the user and has to shoot arrows at the red people. If this is correct then I probably have seen it before (It's liked by me).
There are many other scenarios that also get that error, but I don't know if they would have worked at the time that this one did.
I see that I got some things wrong about the game. I was able to download the .jar file and then open with Standalone - for Windows, running without installation from a USB stick Greenfoot-304.zip.