preventItemClick option is by default set to true. Setting it to false will solve your problem.
<script>
$( '#menu' ).multilevelpushmenu({
preventItemClick: false
});
</script>
However, it is highly recommended to use callbacks as shown below.
<script>
$( '#menu' ).multilevelpushmenu({
onItemClick: function() {
// First argument is original event object
var event = arguments[0],
// Second argument is menu level object containing clicked item (<div> element)
$menuLevelHolder = arguments[1],
// Third argument is clicked item (<li> element)
$item = arguments[2],
// Fourth argument is instance settings/options object
options = arguments[3];
// You can do some cool stuff here before
// redirecting to href location
// like logging the event or even
// adding some parameters to href, etc...
// Anchor href
var itemHref = $item.find( 'a:first' ).attr( 'href' );
// Redirecting the page
location.href = itemHref;
}
});
</script>
Updated fiddle, http://jsfiddle.net/AWJJ4/10/