The intuition here that helped me understand this is that, if you know the search strategy of another player in advance, your best best is to "front run" where they will look as much as possible. So in the ideal case, look in the very next box they are going to look in each round. This guarantees that unless they guess right on the first round, you will get to the gift first.
The rows and columns thing is just a less perfect, but still useful, way for Andrew to front run Barbara's choices more often than the reverse happens.
FYI if you are ever biking here in NL, the thing to remember is that if the "haaientanden" point at you, watch out!, as that means you do not have the right of way.
Edit: The side roads are for cars as well, which means you have a strange turning lane in the middle of the intersection where traffic might back up. A simple roundabout seems like a much better solution here unless the goal is to keep cars moving quickly and the turn lane is rarely used.