The small linkage you are pointing at may be broken. Mine was. However, it will not cause the engine to idle high.
The idle set screw is located at the base of the carb and is factory sealed. It determines how much fuel flow thru the idle jet and is set at the factory. If the plug was removed by a prior owner, then they probably adjusted the screw (which has a needle point end). That can all be reset, so don't worry. That screw all by itself will probably not cause the engine to idle at 2000 RPMs.
The throttle adjust screw is merely a fine tune for the throttle cable. Turn it in or back it out to increase or decrease the fuel to the engine with the foot off the pedal.
This photo shows where to find the throttle adjust and factory idle screws.
The other thing that COULD be a problem is that your throttle cable might be adjusted or set up wrong. You will need to disconnect it and see if the idle can be changed by moving the carb's throttle linkage by hand. Of all the possible problems, that would be the easiest to fix.