The Auckland War Memorial Museum Cenotaph
are putting up basic information on each man in the NZEF (previously it was generally only those who had been killed in the war, or men who were highly decorated) - sometimes this amounts to only the information that was on the nominal roll and/or the CWGC site. Family are able to send information and photos to the museum to be uploaded as well, and also there are sometimes photos from the Auckland Weekly News of the day.
In the case of your chap it says:
Serial No.: 33803
War: World War I, 1914-1918
Enlistment Occupation: Labourer
First Rank: Private
Embarkation Next of Kin: Mrs Mary Ann Burke (mother), Johnson Bridge, County Kildare, Ireland
Embarkation Date: 19 January 1917
Embarkation Unit: 21st Reinforcements Auckland Infantry Battalion, A Company
As it doesn't list date of death etc, we can assume he survived the war.
I've gone through all the Burkes on the nominal roll CDrom and only found one other Burke with NOK listed in Ireland. However, they're in County Clare so I doubt the men are brothers.
Given Name William
Category Nominal Roll Vol. 3
Regimental Number 61526
Next of Kin Title Mrs M
Next of Kin Surname BURKE
Next of Kin Relationship Mother
Next of Kin Address White Gate County Clare Ireland