Get ONLY the count from wp_query without fetching posts

The found_posts property of the WP_Query class is what you’re looking for, which is the amount of found posts for the current query. However, you got a 0 because you set no_found_rows (in the $query array) to true, which means the amount there will not be calculated. I.e.

• WordPress will not append SQL_CALC_FOUND_ROWS to the SQL command for querying the posts. Otherwise, the command would be something like: SELECT SQL_CALC_FOUND_ROWS {the rest of the query}

• WordPress will not execute SELECT FOUND_ROWS() after the posts query is complete. And when it’s not executed, the value of the found_posts property would be a zero (0).

So remove the no_found_rows from the $query array, and the $results->found_posts would have the proper value:

$query = array(
    'post_type' => 'shop_coupon',
    'meta_key' => 'special_key',
    'fields' => 'ids',
);