DOMDocument is part of PHP. See http://php.net/manual/en/book.dom.php
Soon I will add a check in the code to print a user friendly message instead of the error if DOMDocument is not available. I have also updated the documentation, now DOMDocument is listed as a requirement.
In order to use the Mediawiki importer you have to enable DOMDocument on your PHP installation. It is enabled by default on recent versions.
The importer use DOMDocument to read the XML file, so it is not possible to use the importer without it.
Let me know if you net further assistance.