That particular part in the picture is the most buggered up gas adjuster I ever saw. I can adjust mine with my finger tips. If it gets really nasty I suppose you would need a tool. When i first got a FAL I had trouble removing the gas plug due to the previous owner never cleaning the gas system. If you keep it clean things just work better.
I am wondering if the one you have was damaged by someone with a gas cyl wrench, common pliers, or a hammer and punch trying to force it. If it fits on and rotates all is good I suppose. all it has to do is block the oriface.
ETA- look at the front of your gas block at the very small hole. Make sure there is a set screw there that locks your front sight from spinning. I saw your front sight is a bit turned so I thought I'd mention it. The original set screw has a point that mates in the groove on the front sight's threaded shaft.