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It basically reduces the amount of energy that can be absorbed by the atmosphere via friction and pressure waves. The atmosphere is only ~100 km thick from top to bottom. Coming in at a tangent it might have to pass through many hundreds of km of air.
A direct trajectory means a greater likelihood that the impactor will actually hit the surface and will hit with a significant fraction of its mass and energy remaining.
Here's what a 500 kiloton explosion looks like (Ivy King shot, largest fission bomb, 1952) which might give an upper limit example of what could have happened last week:
IVY KING: THE ROYAL ATOM BOMB - YouTube
Well that sounds somewhat plausible, but a head on reentry in a DGIV would vaporize it, whereas a shallower angle allows more of it to survive to hit the surface. Could that apply in this case, or does the scale factor ensure that some high-speed debris will still survive anyways? (Asteroid is a lot more mass than DGIV you know )