It would require developing a payment plugin for it based on the documentation here:
developers.google.com/pay/api/web/overview
The process of developing such plugin is actually quite long. That would require paying a developer at least a thousand euros for him to develop that from what I can see there. Plus, your website needs to be certified PCI DSS level 1 from what I can read there.
Could I just ask how this differs from the two Google payments method that are already included as payment plugins for Hikashop: HikaShop Google Checkout payment plugin and HikaShop Google Wallet payment plugin?