Sorry, but that doesn’t work. (It throws response.statusCode = 403, forbidden.) And it’s not surprising. As I said, the API source server doesn’t allow CORS and is not serving JSONP. So JavaScript calls are blocked.
There are a lot of fine tools for specific jobs, XMLHttpRequest, fetch, request, fs, …, and they work if CORS is set up correctly on the server, allowing you access, or it’s giving you JSONP to handle, but PHP’s file_get_contents is the hammer in your toolbox. If everything else fails, you still can throw this at your problem (provided you have allow_url_fopen).
And I know, it’s not always wise to use (or even throw) a hammer, access might be forbidden (to scripts) for a reason. But if you can read it in your browser, PHP can read, stringify and proxy it to your JS.