I can think of a couple of reasons.
One is that the game might be installed to
C:\Program Files\. It doesn't need to be installed in Program Files and I don't recommend installing there. A better place would be a drive or folder where you have full read/write permission as a non-admin user, like C:\Games (which you should be able to create with the game's installer).
Note: I do not recommend running
any game with admin rights. That is a security risk, and shame on modern vendors who require this.
Another issue can stem from the user data folder. This is identified by the first line in the file
fsgame.ltx in the installation folder. You can view this file in a text editor like Notepad. This user data path should be a valid writable path for the operating system you are using. If it is not such a path, change it so that it is. You might need to copy the file to the desktop, edit it/change it there, and then copy it back to the SoC installation folder if you don't have admin rights. Typically the drive and path are
C:\|ProgramData\Documents\STALKER-SHOC\ for Windows 10 and
C:\|Users\Public\Documents\STALKER-SHOC\ for Vista, Windows 7 and WIndows 8/8.1.
Another possibility is that you are using WIndows 10, and this game needs to install DirectPlay to support multiplayer server management. DirectPlay is deprecated and is no longer supplied with the DirectX that comes with Windows 10, but it is still supported by Microsoft for older games like this 2007 game. It is a quick download if needed, and it only needs to be installed once.
The game will still make changes to your hard drive in the normal use of the game. It will write game-related files to your user data folder: save games, screenshots and log files. It should not ask for permission to do this if the information above is heeded and applied.
Good hunting, stalker.
Edit: Here is more info on admin rights issues with these games:
https://www.gog.com/forum/stalker_series/how_do_you_run_the_game_without_admin_rights