I had a play with the headless Windows 2016 TP3 on Azure late last year and blogged my experience here [1]. You can even run GUI programs on it; I found it useful to run Sys Internals Process Explorer to track what was really happening with the Containers. Obviously there's no desktop with file explorer etc.
Microsoft started down the headless server route quite a while back with the Server Core [0] installations (started with server 2008)
IIRC starting with server 2012 or 2012 R2, all configuration and management functionality was exposed via powershell commandlets, as Server Core was the default installation type and server management was meant to be done via winRM/remote powershell sessions.
The problem is that all server software written with Windows in mind already assume that their interface is a screen and a mouse, and will try to create a main window, dock icon, and show popups when something happens. How will they work on a headless Windows server?
Not all software will work, but plenty of Windows Server services can be controlled via remote procedure calls. Even Active Directory has supported remote administration via LDAP. These protocols can be wrapped around GUI applications or run via Powershell - either of which would obviously run from your client workstation like PuTTY / xterm would when SSHing into Linux.
So, if I understand you correctly, Windows’ new “headless” servers are not actually headless, they simply have an invisible head – it’s still there, you just can’t see it.
It sure doesn't seem like it is there reading the page I linked.
I guess the software you mention that depends on having a desktop will do some combination of not working and working poorly, but they aren't targeting legacy applications with it, they are fleshing out their cloud offering.
[1] https://etrading.wordpress.com/2015/10/13/windows-containers...