The reason this works is that the oncoming person thinks you have not seem them. If someone is coming directly towards you and you think you have seen them before they have seen you, it makes sense that you should move out of their way rather than wait for them to eventually notice you. Also, when you do move, you are guaranteed that they will not move in the same direction (because they would need a little extra time to spot you and perform the evasive maneuver).

I don't think this observation necessarily supports the extramission theory of vision described in the study though. You could achieve exactly the same result by looking at your feet, coving your eyes or wearing a blindfold; anyone coming towards you is still going to get out of your way.