The instructions given result in an error
"Warning: require_once(extensions/StatCounter/StatCounter.php): failed to open stream:"
I checked and there is no StatCounter.php file in the folder.
Topic on Extension talk:StatCounter.com Integration
The extension does not have this file. Instead, it only has an extension.json file. This will only work with MediaWiki 1.25 or newer. So if you want to use the extension, you have to upgrade MediaWiki first - preferably to MW 1.27!
Actually - according to the page - the extension only is compatible with MediaWiki 1.27. So, if you want to use it, you have to upgrade to MW 1.27 - and not to an older version.