How do I access the JavaScript API via a WordPress theme template?
One way would be to write your own AJAX handler in the usual WordPress way and then grab the event list via the CiviCRM API. Untested pseudocode:

// add AJAX functionality
add_action( 'wp_ajax_my_civi_get_event_data', 'my_civi_get_event_data' );
add_action( 'wp_ajax_nopriv_my_civi_get_event_data', 'my_civi_get_event_data' );

/**
 * Get data from CiviCRM
 */
function my_civi_get_event_data() {
    civicrm_initialize();
    $civi_data = civicrm_api( 'event', etc etc );
    $data = my_process_civi_data( $civi_data );
    echo json_encode( $data );
    exit();
}