For security reasons, most server configurations won't let you use file_get_contents on a remote file (different domain name). It would potentially allow a hacker to load code from anywhere on the Internet to your site, then execute it.
Even if your server configuration does allow for it, then I wouldn't recommend using it for this purpose. The standard tool for retrieving remote HTTP data is cURL, and there are plenty of good tutorials out there doing exactly what you should do in this case.
So, let's say you've successfully used cURL to retrieve the JSON array.
$json_output = json_decode($json); // Now the JSON is an associative array
foreach ($json_output['responseData']['results'] as $result)
{
echo $result['url'] . '<br />';
}
Of course, you don't have to echo the URL there; you can do whatever you need to with the value.