I don't understand the new API

You must change the following

  1. Send game_id instead of game

Get the game ID for your game here:

  1. Send the client ID as a header not as a query string

In PHP this is via setting a Header as a curl option

https://www.php.net/curl_setopt

CURLOPT_HTTPHEADER An array of HTTP header fields to set, in the format array('Content-type: text/plain', 'Content-length: 100')

So, (incomplete code snippet):

$ch = curl_init('https://api.twitch.tv/helix/streams?game_id=123');
curl_setopt($ch, CURLOPT_HTTPHEADER, array('Client-ID: YourClientID'));

For example