I’m as keen as anyone on megalithic mysteries and just learned about the Kaimanawa Wall today. I intend to visit it next time I’m near the area.
In the meantime my gut feeling is that it’s natural. It can be seen that the blocks are not offset, which is typical for extra strength, like ordinary brickwork. The main vertical gaps are aligned. The culprit looks to be the large tree inserting roots into soft rock below (i.e. old pyroclastic flows). Trees are extremely strong and could easily put some vertical fractures into what may be flows from two separate volcanic eruptions thousands of years apart, yet, the vertical fractures could be just 100–200 years old.