The names on both of the pages are wrong and should be extension ID instead of client ID or someone did some refactoring and forget to rename the properties and update the doc because i tried the /channels endpoint and i got this response:
{
channels: [{
channel_id: '26428012',
extension_id: '6lf0b37jqhhymqo46o2py5zdwe7vq3',
version: '0.0.1',
activation_state: 'active',
activation_config: [Object]
}]
}
Which contains the property extension_id with the client ID value.