Figured it out. – needed to install more of the PHP framework, specifically php-xml for CentOS. This opens a can-o-worms depending on your OS version yet you will need to install/enable the remi repository beforehand.
Thank for your feedback. I am happy that you could solve it on your own. ASA depends on PHP DOMDocument which is part of the default installation (see http://php.net/manual/de/class.domdocument.php). Of course, there may be some extensions missing for PHP installations that are not standard. But DOMDocument should always be part of PHP since version 5.