So do I first need to buy a supported payment gateway?
Yes, you need to sign up with a supported payment gateway. The reason for this is because Google Pay doesn't process payments, it facilitates it. What I mean by that is it provides you (the merchant) with a secure method of sharing a customer's payment details (through Google Pay) with a payment gateway for processing. In this setup, only saved payment details are only known to Google and the payment gateway.
If so, why won't I accept payments from the gateway itself rather than from GPAY.
The reason that you should consider using Google Pay is that entering payment and contact details can be difficult on a mobile device. Giving your customers access to re-use information that they have already saved on their device makes it easy and convenient for them to complete their purchase which reduces the chances of them from dropping out.