According to the current tax policy of Inland Revenue, gambling is classified as a recreational activity, rather than an income-gaining one. This means that, in the vast majority of cases, Kiwis do not have to pay income tax on their online and offline gambling winnings.
The sole exception to this is professional gambling. If the majority of your yearly revenue comes from gaming activities, then Inland Revenue might label you a professional gambler. In this case, you will have to pay income tax on your winnings.