AFAIK, the bore axis is the distance from the center of gravity to the center line of the bore. When a gun is fired, the forward movement of the bullet causes the backward movement of the barrel/breech unit. That is not straight back because the other parts of the gun are not on the bore line, but (usually) below it, resulting in the gun pivoting so the muzzle rises. With a handgun, the center of gravity is not only that of the gun, but of the gun/hand unit.
The more of the mass of the gun is directly on the bore line, the less upward recoil there will be and the more the recoil will be straight back. To achieve closer to straight back recoil in rifles, the stock is often designed so more mass is behind the barrel, resulting in the need to move the pistol grip to the bottom of the gun. This, not "shooting from the hip", is the real reason for rifles with pistol grips.
Jim