Server OS. A post below which can be found on Microsoft Forum is also helpful.

You cannot change this behavior. This is by default and should not be changed. Screensavers can be killing to the system as many resources, processor and memory, can be used by screensavers. Therefore it is not a best practice to enable screensavers on terminal servers and also explains the behavior of Windows Server 2008.

Link from Windows Server Forum:Screen saver not working on TS2008


 

Screensaver does not work on Server OS if users are connected via RDP or via ICA

Screensaver won't be started if user is connected to Windows Server 2008/2012 via RDP or ICA even if the screensaver can be started locally. This is by OS design to reduce the resources usage b disconnected TS sessions

The registry setting of SetDisplayRequiredMode mentioned in the following article resolves the issue only for Desktop OS due to gfxmgr.exe which is blocking screensaver. This does not work for Server OS because gfxmgr.exe does not exist.

http://docs.citrix.com/en-us/xenapp-and-xendesktop/7-6/xad-whats-new/xad-xaxd76-knownissues.html

• Screen savers and the power-save option are disabled in sessions. Edit the registry and create the following DWORD value:

  HKLM\Software\Citrix\Graphics\SetDisplayRequiredMode = 0
  

  This change does not prevent the remote machine screen saver or power save mode from coming on. If the power save mode comes on, the remote session is not updated until the user provides input (mouse/keyboard), but the screen will not be blanked. [#380550]