Cheney was reportedly using #7 1/2 shot, a standard quail load, which are .090 diameter (nominal).
Shells loaded with large shot (buckshot) have few individual shot, logically enough, compared to smaller shot. 6 000 Buck weigh an ounce, or an individual 000 Buck weighs 1/6 ounce. It takes about 350 #7 1/2 shot to weigh an ounce, or 2,300 #12.
Cheney was using a 28 gauge shotgun, a relatively small-bore gun. Standard field loads for the 28 gauge contain 3/4 ounce of shot, or about 275 individual #7 1/2 shot.
Shotgun barrels have a constriction at the muzzle known as a "choke" that ranges from Full choke (the tightest) to Cylinder, essentially no choke. The effect of a choke is to control how quickly the shot charge spreads after it leaves the muzzle, and it's measured at a standard 30 yards from the gun. Cheney's gun has two barrels, most likely an Improved Cylinder and a Modified. By definition, an Improved Cylinder choke will place 50% of it's shot charge within a 30" circle at 30 yards, while a Modified will put 60% there.
Most field load shotgun shells, regardless of gauge, generate a muzzle velocity of about 1,200 fps (feet per second). The primary difference between gauges is the weight of the shot charge it launches. A field-load 12 gauge shell loaded with #7 1/2 shot will launch about 400 shot compared to the 28's 275, but the individual shot will be travelling about the same velocity and have the same energy. Small shot lose velocity (and energy) relatively quickly as they move downrange, and beyond about the 30-yard mark will have slowed sufficiently to be ineffective at killing a flying quail due to their inability to penetrate significantly.
If I have left out any pertinent facts feel free to add them, but we need to separate facts from speculation.
If, in fact, the victim was struck by about 200 shot from Cheney's gun he couldn't possibly have been 30 yards from the gun.