You are not logged in.
When Googling around I didn't find a script for this exactly, but was able to piece one together from other hints on this forum and elsewhere, so wanted to share the solution in case anyone else looks.
From the AppleScript Editor save as an Application with the "stay open" option, then make sure you launch and check the "Open At Login" option from the dock.
You can just insert more if-then blocks if you want to kill more applications. I just often leave Skype running when I don't intend to, so that is the code you see.
As shown, the script only checks every 5 minutes, which is precise enough for me. Obviously, you can reduce that number, at the cost of the script waking up more frequently and using some CPU cycles.
-- Script to quit certain applications when ScreenSaver is active
tell application "System Events" to set appNameIsRunning to exists (processes where name is appName)
-- check if screen saver and Skype are running
if ApplicationIsRunning("Skype") and ApplicationIsRunning("ScreenSaverEngine") then
tell application "Skype" to quit
-- don't check for another 5 minutes (converted to seconds)