I can see there are some questions about why I clicked the Multiplayer button in FEAR. For one thing, the
FEAR game card said that FEAR has working Multiplayer for LAN. I wanted to see if there was some kind of bot match in FEAR's multiplayer mode. However, I was not warned that FEARMP.exe would install remnants of SecuROM in the Registry and AppData folders.
With help from this thread, I was able to get rid of the DRM remnants. But I was also hoping that GOG would have released a new version of FEAR with the FEARMP.exe file either deleted or disabled. I wanted to make sure other gamers wouldn't have to deal with this SecuROM remnant problem. Unfortunately, since GOG still hasn't updated FEAR yet, the only way to fix this problem is just to delete the FEARMP.exe file.
It also saddens me that this multiplayer oversight on GOG's part is causing some people to be hesitant to buy FEAR. FEAR in itself is an excellent game; it's one of my favorite FPS games. It's just unfortunate that GOG forgot to check the multiplayer to delete the rest of the DRM. But I will repeat that FEAR singleplayer is fine and does not have SecuROM.