He should have used a diagram or two. Here's a very simple one (but it ignores the optical line through the scope or sights):
In the figure, the shooter is compensating (elevating) for the line of sight distance. If he were to elevate in all three shots only for the horizontal distance (like in the level shot), his shots would be much closer to on target. There might be some smaller effect errors due to other things, but I believe this is the biggest source of shot error in the described scenario.