My guess would be that mod_rewrite is a module that needs to be compiled and linked into the server (Apache). I would ask on a support forum for whatever specific package you use (WAMPP, XAMPP, LAMPP, etc.).
Have you tried enclosing the rewrite section in .htaccess with something like
<IfModule mod_rewrite.c> ... </IfModule>? I think that's the right syntax, but you should check. You might have mod_rewrite, and just need to explicitly invoke it.