That "link to your article" is a pingback, and is a valid comment type in WordPress.
There are two issues:
- Apparently, your Theme isn't configured to display pingbacks/trackbacks in the comment list
- The WordPress function
get_comments_number() counts all comments, rather than just comment-type comments. You can filter it, if you want, so that it returns just the number of comments, rather than the total number of comments and pings.
Use something like the following (in your functions.php file):
/**
* Filter 'get_comments_number'
*
* Filter 'get_comments_number' to display correct
* number of comments (count only comments, not
* trackbacks/pingbacks)
*
* @link http://www.wpbeginner.com/wp-tutorials/display-the-most-accurate-comment-count-in-wordpress/ WPBeginner
*/
function mytheme_comment_count( $count ) {
if ( ! is_admin() ) {
global $id;
$comments_by_type = &separate_comments(get_comments('status=approve&post_id=' . $id));
return count($comments_by_type['comment']);
} else {
return $count;
}
}
add_filter('get_comments_number', 'mytheme_comment_count', 0);
Then get_comments_number() will return just the number of comments.
EDIT:
Your Theme (which, by the way, hasn't been updated in the Repository in almost two years) is designed only to output comment-type comments. See here, in comments.php:
<ol class="commentlist">
<?php wp_list_comments('type=comment&callback=cleanr_theme_comment'); ?>
</ol>
You'll either need to modify the code, or switch to a Theme that supports listing trackbacks/pingbacks.