I see what your problem is.
Basically, in setting %path% to C:\Program Files\Java\jdk1.6.0_25\bin, you imply that manifest.txt, Game.class, Core.class, etc. are all in the same directory. What I'd have done there is navigate to the folder with Game.class in, then invoked C:\Program Files\Java\jdk1.6.0_25\bin\javac.exe or w/ever the compiler/packager is. I think it's javac.exe, anyway. Always works for me.