Check if an event is in a particular parent category -- https://eventespresso.com/topic/check-if-an-event-is-in-a-particular-parent-category/

event_taxonomy_check.php

<?php
//* Please do NOT include the opening php tag, except of course if you're starting with a blank file

add_action( 'AHEE_event_details_before_post', 'my_custom_event_category_html' ); // can use a different hook here
function my_custom_event_category_html( $post ) {
  $term_list = wp_get_post_terms($post->ID, 'espresso_event_categories', array( "fields" => "all" ) );
  // print_r($term_list); // useful for debugging, commented out
  foreach ( $term_list as $term ) {
    if ( $term->parent == '116' ) { // parent category ID
      echo '<h3>ABC</h3>';
      return;
    }
    if ( $term->parent == '115' ) { // parent category ID
      echo '<h3>XYZ</h3>';
      return;
    }
  }
}