How to use get_categories() with Event Organiser plugin

Event categories are terms in a custom taxonomy, ‘event-category’, so you should use get_terms instead:

//Args for which terms to retrieve
$args = array('type'=> 'post', 'order' => 'ASC', 'hide_empty' => 1 );

//Array of taxonomies from which to collect the terms
$taxonomies = array('event-category');

//Get the terms
$terms = get_terms( $taxonomies, $args);

//loop through the terms and display
foreach($terms as $term) {
    echo '<li><a href="#tabs-content-'.strtolower($term->term_id).'" title="' . sprintf( __( "View all posts in %s" ), $term->name ) . '" ' . '>' . $term->name.'</a></li>';
    array_push($cat_list,"$term->term_id");
}

If you want to get terms for both the ‘category’ and ‘event-category’ taxonomy then you can add ‘category’ to the $taxonomies array.