Get posts from multiple tax terms

I honestly don’t see how that works at all since get_the_term_list returns an HTML string.

First, you need get_the_terms and wp_list_pluck.

Second, you need a tax_query. That {tax} = {term} pattern is deprecated.

$this_post = $post->ID;
$args = array(
    'post_type' => 'dir_entry', 
    'posts_per_page' => 10, 
    'orderby' => 'date', 
    'order' => 'DESC', 
    'post__not_in' => array($this_post), 
  );

$terms = get_the_terms($this_post,'post_tag');
if (!is_wp_error($terms)) {
  $terms = wp_list_pluck($terms,'term_id');
  $args['tax_query'] = array(
    array(
      'taxonomy' => 'post_tag',
      'field' => 'id',
      'terms' => array_values($terms)
    )
  );
  $query = new WP_Query($args);
}