<?php
$terms = get_terms( array(
    'taxonomy' => 'genre',
    'hide_empty' => true,
) );

$today = time() - 86400;

foreach($terms as $term) {
    $query = new WP_Query( array( 'meta_key' => 'event_date', 'meta_value' => $today, meta_compare => '>=', 'tax_query' => array( array( 'taxonomy' => 'genre', 'field' => 'term_id', 'terms' => $term->term_id, ), ), ) );
    if (($query->found_posts) > 1) {
    echo '<li><a href="/genre/' . $term->slug . '">' . $term->name . '</a></li>';
    }
} ?>