<?php
require_once 'vendor/autoload.php';
$client = new Google_Client();
$client->setApplicationName('My YouTube Client');
$client->setDeveloperKey('YOUR_DEVELOPER_KEY');
$youtube = new Google_Service_YouTube($client);
$videoId = 'VIDEO_ID';
$videoResponse = $youtube->videos->listVideos('statistics', array(
'id' => $videoId,
));
$video = $videoResponse[0];
$likes = $video->getStatistics()->getLikeCount();
$dislikes = $video->getStatistics()->getDislikeCount();
echo "Likes: $likes, Dislikes: $dislikes";
Если данных нет, значит вам не положено их видеть.