In the image below, the red areas show where the Westerners fixed their stares, while the blue areas were preferred by the east Asians.
It could be that it's impolite in East Asian cultures to make direct or prolonged eye contact, and focusing on the centre of the face is simply a way of avoiding a social faux-pas. The second and more interesting theory, is that these strategies reflect general differences in the way that Westerners and East Asians view the world around them.
Some psychologists have suggested that Westerners view the world in an analytic way, by focusing on key features, while East Asians have a more holistic perspective where an object's context is just as important as its parts.
Reference: PLoS ONE doi:10.1371/journal.pone.0003022