The sound absorption is good if you are in the same room as the problem noise source - like in the ear test, or maybe in a concert hall, where the thing you are listening too can bounce around or echo between the walls, and these reverberations cover the clear original sound. The sound absorbing material - those chunky panels in a concert hall, for low frequency,
or maybe fabics for high frequency
(even having a concert hall full of people helps a lot) actually change the angle the sound is reflected back at, so instead of bouncing back across the room, it rattles around between the chunky panels, or the fibres of the fabrics etc. until its energy is lost.
Problem is, the energy of the sound travelling in the air is lost into the panel, fabric etc. as vibration.
So, if you are in a different room from the problem noise source, having the wall in between absorb the sound doesn't help, as it will still tend to make the wall vibrate, and transmit the sound to the other room where you are.
So the two layers of plaster board works because it is heavy, and hard to start vibrating.
The sound insulation does absorb any sound that has got into the cavity in the thickness of the stud wall.
The staggering studs method separates the two sides of the wall, so that if one side starts vibrating, the studs don't transmit that vibration to the other side, and the sound insulation weaving inbetween stops the vibration passing through the air cavity in the stud wall.
Solid plastered block wall is good at stopping air borne sound, but very bad at structure borne sound - if some one hammers a nail into it
the sound comes through really bad. Same thing with high heels clicking on a concrete floor above.