Not a new answer (don't have the rep to comment yet) so upvote the answer above.

1. The first traversal ends up with the point at about 0.1, 0.52 with a search point of 0.38, 0.6 (all numbers guestimated). So that is an error of about 0.29.

2. We then have to backtrack to the previous node and see if that hyperplane is closer than the error.
   At 0.04 away it is so we have to check it as well we find the point 0.42, 0.641 which would be only 0.08 away.

3. We now go to the root that hyperplane is 0.15 away so nothing on that side could be closer.

If you are wondering about best and worst case The time complexity for a 1-NN (nearest neighbor) search using a KD tree (i.e. balanced binary tree) is in what range?.