What is the term shortlink structure?

Well if you are referring to what are the query string keys are, it will depend on the taxonomy you are working with, for

• categories: you are looking for ?cat=cat_id
• tags: you are looking for ?tag=tag_slug
• custom taxonomy: it depends on the slug of the tax but it will look like ?taxonomy_slug=item_slug

Check the definition of the default WP query vars keys for more info

EDIT

As per you comment, I thought I would share this too. If you need/want to search by term_id (regardless of custom tax or not) you would need to add a custom query string (query vars) and modify the main query to do so.

Here’s how you could do this

// Add your custom query var so WP can listen for that query string too
add_filter( 'query_vars', 'my_add_custom_query_vars' );
function my_add_custom_query_vars( $vars ){
  $vars[] = 'my_var';
  return $vars;
}


// Then modify the query to include all taxonomies, searching by tax ID
add_action( 'pre_get_posts', 'my_custom_query' );
function my_custom_query( $query ){
  $my_id = absint( get_query_var( 'my_var' ) ); // retrieve the var defined above

  $tax_query_args = array(
    array(
      'field'         => 'term_taxonomy_id',
      'terms'         => $my_id,
    ),
  );

  $query->set( 'post_type', 'any' );
  $query->set( 'tax_query', $tax_query_args );

}

My example could be expanded to listen for multiple term_id so you could use a query string like ?my_var=1,2,3 to return any posts within term_id 1 OR 2 OR 3 or ?my_var=1+2+3 to return any posts within term_id 1 AND 2 AND 3. But as a general basic concept, this is how you would do it.