****UPDATE***** I have updated the custom wakeword project and here is the latest version https://www.hackster.io/shiva-siddharth/multiple-custom-wakewords-activation-of-google-assistant-d0c986 this is a much better improved of this project.****
Normally, you cannot voice activate Google Assistant SDK on Pi Zero W. By the method shown, not only can you voice activate Pi Zero W or Pi 3, you can voice activate it with a custom wake word using Snowboy.
As the project involves lots of intricate steps, I have created a ready to use image with all the necessary changes made. It also contains all the requisite files and installations to get you started.
Links to the ready to use Raspbian image: https://goo.gl/K9uyqZ
To install the requisite audio drivers and to authenticate the Google Assistant, follow the instructions listed in a file that you can find inside the project folder located in /home/pi directory of the image
Reference link for creating auth credentials: https://developers.google.com/assistant/sdk/prototype/getting-started-pi-python/config-dev-project-and-account