Sorry to necro this, but I came bearing a solution. For some reason, the manifest headers in the game's EXE file is set to request admin when run, but there is a way around it.
Shadow of Chernobyl is the easiest, just downgrade the game to version 1.0004 or 1.0005 and its EXE doesn't require admin privileges. It's recommended to run these versions for single player anyway since the 1.0006 version, although official, was recalled due to extra bugs introduced. A lot of mods also don't work with 1.0006. There are instructions to do this
over here.
For Clear Sky and Call of Prypyat, modify the game's shortcut, make sure to remove any compatibility options set by the GOG installer, or just make a new shortcut. Then in the target box paste this
in front of the text already there.
C:\Windows\System32\cmd.exe /min /C set __COMPAT_LAYER=RUNASINVOKER && start ""
It needs to be pasted exactly as shown. It should look something like this:
C:\Windows\System32\cmd.exe /min /C set __COMPAT_LAYER=RUNASINVOKER && start "" "D:\Stalker Call of Pripyat\Stalker-COP.exe"
The icon will change to the CMD icon, but you can change it back with the change icon button.
Now the game will start without requiring admin privileges to run.