I'm with Harry, I can't see any real point to that wall! A better solution would be bring the neighbours gate forward and make it bigger to go right across to your side with provisal that you need occasional access for maintenance.
FWIW, It doesn't look that way to me. The wall (Except for that pier thing) appears to be entirely on the OP's property.
I'm not an expert, and plans are not fully accurate, but if you use the plan as the guide then the existing retaining wall is on boundary and what the neighbour is doing is mimicking the boundary with their new wall - which means that half of the wall is on either side of the boundary.
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