Hello,
Internet Explorer is required not only for the installer GUI, but also for the Web interface Customization Tool, a visual application that allows you to configure the Web Interface, and also backup and restore Web Interface configuration. Moreover, all components of Adaxes rely on the WIndows ADSI component, multiple .NET classes and the Kerberos protocol. As far as we know, not all of that is fully available in Server Core.
Currently, we do not support installing any component of Adaxes on a Server Core.