This is quite a simple system : Its only requires redstone torches, repeaters and redstones.
The point of the system is simply to invert the redstone torches that activated all the pistons by doing in the video.
I use redstone torches in the system so the person that wants to replicate it wont swear that his system is always activated. Keep in mind : The second floor and third floor are inverted by the redstone torch as the first floor is activated by the lever. I didn't use a t-flipflop because I only wanted to use a lever but, the system can have a flip-flop if you add it on the first floor.