John Matheson died in June 1947 aged 55 or 56 and is buried in Onerahi cemetery in Whangarei. The designated dates for a death resulting from active service in WW2 to be counted as a war death are from 3 September 1939 to 31 December 1947. The inclusion of John Mathieson in the official tally indicates that he died as a result of as injuries or illness incurred while on active service.
According to the Cenotaph database and his headstone he was awarded the Military Medal and had served in WW1, though there is no record of him serving in the New Zealand forces during that conflict. I suspect he served in the Home Guard in WW2, and in other forces (probably British) in WW1 where he won the Military Medal.
Cenotaph also states that he was the son of George and Margaret Mathieson and husband of Jessie Mathieson (nee Rennie), of Whangarei.
Auckland War Memorial Museum Cenotaph database
Photo by Mary Farrelly via findagrave.com