From your video the center portion on your compressor is NOT turning so the electric clutch is not engaging and the compressor will not turn and compress the freon...
You should have either one or two wires connecting to the compressor...
If you have one wire then if you connect +12v from the battery with the AC mode on, with the engine running and the the settings at the coldest position and the center of the compressor starts to turn then you may have a wiring problem or a low freon charge...and you do not have a bad AC clutch...
If you have two wires connected to your compressor ...one of them will connect directly to the body of the compressor and the other will connect to the clutch coil and you need to connect +12v to that one to get the results above...
If the clutch clicks the compressor clutch is OK and the chances are you are low on freon or possibly have a blown fuse...
The wiring on most cars have a switch on the AC lines that if the freon is too low it will NOT allow the AC clutch be engaged...