That is often called the " High mount " style of shotgun shooting. The advantage is that the stock does not have to really be fitted to the shooter's face, the shooter does not feel recoil directly under his eye, where he is likely to flinch first, and with the front bead in the lower peripheral vision of the shooter, a reasonable pattern is going to take the bird, anyway.
To do this kind of shotgun shooting. hold your head comfortably upright, and bring the shotgun to your shoulder, rather than to both your shoulder and cheek. To reach crossing targets, your entire upper body moves like the turret on a tank. Elevation is done with the hands, or for some, by leaning back or down with the upper body.
For shooters used to shooting the more traditional "low mount " position, where the stock comes to the face and the shoulder at the same time, this style of shooting is difficult if not impossible to do. Its takes much practice to change your mount, and more practice to have the confidence that your pattern will kill birds.