Showing User’s Post Counts by Custom Post Type in the Author.php?

Here I’ve modified the code from URL you’ve given.

function _yoursite_get_author_post_type_counts() {
    static $counts;
    if (!isset($counts)) {
        global $wpdb;
        global $wp_post_types;
        $sql = <<<SQL
        SELECT
        post_type,
        post_author,
        COUNT(*) AS post_count
        FROM
        {$wpdb->posts}
        WHERE 1=1
        AND post_type NOT IN ('revision','nav_menu_item')
        AND post_status IN ('publish','pending', 'draft')
        GROUP BY
        post_type,
        post_author
SQL;
        $posts = $wpdb->get_results($sql);
        foreach($posts as $post) {
            $post_type_object = $wp_post_types[$post_type = $post->post_type];
            if (!empty($post_type_object->label))
                $label = $post_type_object->label;
            else if (!empty($post_type_object->labels->name))
                $label = $post_type_object->labels->name;
            else
                $label = ucfirst(str_replace(array('-','_'),' ',$post_type));
            if (!isset($counts[$post_author = $post->post_author]))
                $counts[$post_author] = array();
            $counts[$post_author][] = array(
                'label' => $label,
                'count' => $post->post_count,
                'type' => $post->post_type,
                );
        }
    }
    return $counts;
}
$user_id = get_current_user_id();
$counts = _yoursite_get_author_post_type_counts();
$custom_column = array();
if (isset($counts[$user_id]) && is_array($counts[$user_id]))
    foreach($counts[$user_id] as $count) {
        // $link = admin_url() . "edit.php?post_type=" . $count['type']. "&author=".$user_id;
        // admin_url() . "edit.php?author=" . $user->ID;
        // $custom_column[] = "\t<tr><th><a href={$link}>{$count['label']}</a></th><td>{$count['count']}</td></tr>";
        echo $count['label']. "  ".$count['count']."<br />"; 
    }
}

I’ve not tested but it’s based on the code from given URL. I’ve just echoed it to verify if the correct data is being displayed. Further you can do what’s you required for you actual requirement.