The diaphragm you can see through the hole is not the pump diaphragm....It moves because when you choke the carb all the suction from the piston going up pulls fuel through the inlet needle...When you open the choke there is not enough suction to do that...The diaphragm on the other side is the pump diaphragm, it is activated by the crankcase pulses, completely separate...The pump fills the cavity under the other diaphragm, then air flowing through the carb pulls fuel through the little holes and high speed nozzle, just like a cheap paint gun...When the cavity empties the diaphragm is pushed down by atmospheric pressure and lifts the lever that lifts the inlet needle to let more fuel into the carb...
Choking the carb lets enough fuel into the engine to run for a few seconds and stop if the pump isn't working because of a pulse leak...