According to Wikipedia, Windows Server Core is a "minimalistic Microsoft Windows Server installation option, debuted in Windows Server 2008".  As such, Server Core does not have the traditional Windows Explorer shell (or "Windows Desktop Experience") and, depending on the version used, may or may not have any Remote Desktop support.  Typically Server Core is managed via command-line interface windows, remote Microsoft Management Console connections, various remote server administration tools, and PowerShell.  The intent behind Server Core appears to be at least two-fold, viz., 1) eliminate the massive overhead represented by the Desktop Experience GUI, and 2) reduce the "attack surface" of the operating system (again, per Wikipedia, one Microsoft engineer estimates that 70% of the vulnerabilities plaguing the OS over the last five years would not have affected Server Core). 


LISTSERV has not been tested in Server Core environments, but given that LISTSERV is not a traditional Windows GUI application, it should not have any problems per se running under Server Core.  The difficult part would be installing LISTSERV from the current GUI-based InstallShield installer.


In Windows Server 2016, an even smaller Server Core implementation known as Nano Server is available.  Nano Server appears to be designed for Windows Server Containers and Hyper-V Containers.  At this time it is unknown whether LISTSERV will run in the Nano Server environment.


However, L-Soft can provide all of the necessary LISTSERV files in a compressed .ZIP archive and LISTSERV can be configured manually; this is, in fact, the way LISTSERV was originally delivered for Microsoft Windows in 1994.  If this type of installation is required, please contact the Support department and we will provide the manual installation kit.