Just figured the thing out. There is even a video describing the drag and drop functionality BUT there isn’t a single WP_query demo! After a week, I noticed in the backend the link for ordering posts/pages (Sort by Order). The link:
<a href="/wordpress/wp-admin/edit.php?post_type=competence&orderby=menu_order+title" class="current">Sort by Order</a>
You can see the query ordering:orderby=menu_order+title. So using this in a WP_query sorts the custom posts in the correct maner.
My example:
$new = new WP_Query(array( 'post_type' => 'competence', 'orderby' => 'menu_order', 'order' => 'asc', 'showposts' => '100' ));
while ($new->have_posts()) : $new->the_post();
You’r welcome 🙂