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,

http://syntensity.com/static/bb/client.html

In fullscreen mode the mouse cursor works ok (at least in browsers that support mouselock).