Why does Thrust Reverser need to be operative during the cargo door operation?
“It is stated that when the Electric Pump push button is depressed, the electric pump is automatically running as long as the cargo door selector valve is set to either OPEN or CLOSE position”

This is not correct. Cargo door operation will automatically energize the Elec Pump while it is in the OFF position. (not depressed)

“My question here is why thrust reverser ENG#2 needs to be operative during cargo door operation”

It doesn’t need to be operative. It needs to be Not Inhibited,  in case there is a malfunction. 

The cargo door uses the Yellow system. It is designed to be used on the ground even with the Electric Pump in the OFF position. The pump will come on automatically in this case to supply hydraulic power to the cargo door. It will inhibit all the  other items on the yellow system to insure adequate hydraulic power to the cargo door.

BUT......If there was a malfunction in the Cargo Door system while in flight, it could possibly cause the Yellow Elec Pump to engergize while it is in the OFF position. If that were to happen, it is designed to inhibit all items on the Yellow system. That would be bad, so they designed the switch to inhibit everything except Alt Brakes and #2 Reverse.

This situation could only happen if the Yellow Elec Pump was automatically commanded ON while in the OFF position.