I think the engine multiplies mouse movement by some factor, so the OS cursor diverges from the game cursor. But in fullscreen+mouselock mode it should work fine, not sure why not in that link, but here is a link to another wip port of the same game engine to JS/WebGL,
It's by far the most advanced WebGL FPS shooter I've seen so far - http://www.webgl.com/2012/05/webgl-game-cube-2-sauerbraten/