As you are using PHP 5.5+ versions, the old PHP 4 things will throw errors … of course. The error comes from – as you can read – the WordPress importer plugin, which is some kind of badly treated step child of WordPress.
plugins/wordpress-importer/wordpress-importer.php:38
One solution is to use our fork with fixes from wecodemore/GitHub, where you can add your patches as Pull requests. You can also pull it via Composer.
The other solution is to try the Humanmade rewrite on GitHub instead, tough I have no idea how final it is. I have filed a Pull request to get Composer support, but I guess it is unmaintained currently.