The main points are on pages 2 to 3. They describe the audio signatures of gunfire. These include:
1) the muzzle blast:
2) the shock wave phenomenon:
3) relative timing of shock wave and muzzle blast:
The paper then presents a case study on how these facts can be used in a forensic investigation to estimate the approximate distance a rifle was fired from a camera that picks up both the ballistic shock wave and the muzzle blast. In the example from the West Bank, the audio shows the initial sound of the shock wave followed by the muzzle blast approx. 310 ms later, as well as what look like some reverberations or echoes.
The vast majority of recordings of gunshots, e.g. on YouTube, are recordings taken from close to the rifle, either to the side or behind it. Recording from that location will not pick up the ballistic shock wave. To get that on audio, the camera/microphone needs to be in the path of the bullet, in front of the rifle, and not behind the target. This guy doesn't seem to be aware of that.
The first sound is the ballistic shock wave, which reaches the camera almost instantly as the bullet passes next to, or above, the camera faster than the speed of sound. The second sound is the muzzle blast, which travels much slower, at the speed of sound. The two sounds are the sound of the bullet breaking the sound barrier, and the sound of the explosion from within the rifle when the bullet is fired. The reason there are two sounds is that they have two different sources, separated in time. It takes a fraction of a second for the sound of the muzzle blast to "catch up" to the bullet.
Yes, that is why the recording picks up both the shock wave and the muzzle blast. In the example of a .30-06 that he uses as a comparison, there is only one sound, the muzzle blast, because whoever recorded that sound was probably recording from very close to the shooter's position, not in the path of the bullet. If he had used a recording of a .30-06 where the camera was located somewhere along the path of the bullet, he would see 2 sounds: the shock wave and the muzzle blast.