As Lightness Races in Orbit suspected, it does seem that the webserver is blocking PHP's request.
Using cURL instead of file_get_contents()
reveals the details:
HTTP/1.0 403 Forbidden
Scripts should use an informative User-Agent string with contact information, or they may be IP-blocked without notice.
A web browser sends a valid User-Agent header in its request, which is why the page loads OK in your browser but not in PHP.
In my tests loading this URL in PHP, sometimes it succeeds with an HTTP status code of 200, other times it fails with 403. Notice that the error message says scripts may be blocked (ie. sometimes they may not be blocked).
Edit
See this question for more info: How to get results from the Wikipedia API with PHP?