Since warfare is a major way in which borders are formed it's reasonable that a trend would show in the orientation of international borders.

It's interesting that the graph shows an east/west orientation in Europe and Asia, where borders grew more organically, and a more even distribution in South America and Africa, where the borders are largely remnants of colonialism. Take it with a grain of salt though, I don't think there is a general correlation between direction and ease winning battles or wars.

Going north or south is more difficult for longer campaigns. This is mainly due to climate. When going east or west, the temperature generally stays in the same range, and you stay in the same general climate overall. An empire originating in Italy, for example, can easily survive in a mediterranean climate, can adapt for warmer temperate and cooler subtropical forests, and can adapt to plains/savannah, but will have difficulty adapting to taiga (such as northern Europe), extreme desert (such as the Sahara). This is a significant contributor to why many empires are much wider east-west than north-south. This isn't so much a function of combat though, although the fact that east and west will generally yield more familiar terrain is a definite factor in battle.

I'm looking at this from a primarily climate based perspective. I don't have that many good historical examples, as my knowledge is more scientific than historical, but just from looking at maps of empires, there is a clear bias towards eastward and westward expansion.