From November 2018 Google has been charging GST on ad-words through Google New Zealand Limited. Google adwords is required to charge 15% GST on its services. You should see GST column on Invoices issued after November 2018.

GST Registered businesses can still claim back GST on adwords. However, they need to increase spend by 15% in order to get back to previous level of advertising budget.

See comments by minister Stuart Nash in this article