I didn't read the article in your link, but I came up with the idea myself(Trying some 1-D special cases and then a proof by contradiction). Then, I wrote the code based on it, only to find it not working. So, I re-examined the idea, and finally figured out why it was wrong in this problem.

The reason is: In this problem, the absolute deviations at a certain position is weighted by the number of points that are actually at this position. If we have a bunch of coordinates, and at each coordinate, there is exactly one point, then the optimal solution is definitely the middle point. But now, in a single row or column, there may exist multiple points. So, the optimal solution should be biased towards the region with denser points.

As a simple example, suppose the coordinates are 0, 50 and 100. If there are one point at each position respectively, then the meeting point would be 50, definitely. But suppose there are 1000 points at 0, and other two points each at 50 and 100, respectively. Of course, you'll have to choose 0 as the meeting point. Otherwise, the 1000 points at coordinate 0 will have to move to at least 50.