Sort new column in Users wp-admin

If orderby equals post_count, WordPress will always work with posts from the default post type post. What you can do is, try to modify that part of the query for this specific case.

Something like this should work:

add_filter( 'query', 'smartwp_sort_last_login_column_query' );
function smartwp_sort_last_login_column_query( $query ) {
    if ( ! is_admin() ) {
        return $query;
    }

    $orderby = isset( $_GET[ 'orderby' ] ) ? $_GET[ 'orderby' ] : false;

    if ( $orderby !== 'Listings' ) {
        return $query;
    }

    if ( stripos( $query, 'SELECT post_author, COUNT(*) as post_count' ) !== false ) {
        $query = str_replace( '( post_type = \'post\' AND', '( post_type = \'job_listing\' AND', $query );
    }

    return $query;
}

What this does is tell WordPress to count the posts from the custom post type job_listing. Please note, that this only works for your specific case.

Make sure to fully test it, as this is the query hook, which is executed on every database query WordPress makes.