Ordering posts in Search & taxonomy by post_meta

You have a couple of issues with the code you are trying.

To check the query is for your CPT archive: You are using $query->is_post_type() but it doesn’t work (as far as I know, its not even a function). Instead you can use either:

if (is_post_type_archive('business')) {...}

or (if its not only on the archive page)

if ($query->get('post_type') == 'business') {...}

To order by meta value in pre_get_posts, you need to set the meta_key as well as the orderby (and optionally order).

Complete Function: Applying these to your “custom_special_sort” function, we get:

function custom_special_sort( $query ) {

    // if is this the main query and is this post type of business
    if ( $query->is_main_query() && is_post_type_archive( 'business' ) ) {

        // order results by the meta_key 'featured_listing'
        $query->set( 'meta_key', 'featured_listing' );
        $query->set( 'orderby', 'featured_listing' );
        $query->set( 'order', 'DESC' );
    }
}
add_action( 'pre_get_posts', 'custom_special_sort' );