“Normal”, in this case, means perpendicular to a plane. So if the force is “normal” to the sides of the square tube, then it hits perpendicular to a flat side. That means that the impact side is in compression, the far side is in tension, and the 2 aligned sides are in bending “the strong way”.
If it hits on a corner, then the tendency is for the impact corner to go in, which it can easily do by pushing the 2 side corners outward, which in turn wants to pull the far side corner in toward the center. The impact corner and opposing corner are growing closer together and the cross section aligned with the force is shrinking, and there is really VERY little of the cross section in tension or compression while the bending forces are mostly “the easy way”.
Round is somewhat in between the 2 extremes. It has consistent behavior regardless of orientation of the force, and there are always portions in tension and resisting the bending. And even if the impact point collapses and puckers on each side, your generally left with a “D” like shape so there is still some reasonable cross section, particularly if the cage uses triangulated nodes so that the nodes strongly resist being pulled together. Round tube only collapses when it’s severely bent.
Try this, take some poster board and form a square tube with sturdy tape at the intersection. Place it across some chair backs or something and push on it “normal” to the walls. It should resist a fair bit, even surprisingly well. Now turn it 45* and do the same thing, and you should see it readily collapse. Finally, roll it into a tube and repeat both steps. This is not an exact model, but it should make the relationships pretty obvious.