Good question, and the answer is 'I don't know'. I started to track this down, but can't explain it well. I do know that it is not a mistake.
I have done a whole slew of these DFTs on similar aperiodic patterns, and this exact feature appears in many/most of them. See, for example,
The pattern for which this is the DFT is very simple, so it is a good case to consider. Roughly speaking, "there is zero amplitude when the phases in the x and y direction add up to +-pi, iff the signs of the phases are the same". This must have something to do with the symmetries of the patterns, e.g. whether they have mirror/rotation symmetries. But I haven't pinned that down.