Google have been requiring GTINs as part of Google shopping feeds since 2015.
They state: ‘We recommend providing clear product identification, as this helps Google to match offers to products, and to match products to relevant search queries. You can improve Google's understanding of products by using unique product identifiers like Global Trade Item Number (GTIN™), Manufacturer Part Numbers (MPNs), and brand names’ ‘This helps us surface relevant, accurate results on Google Shopping; in fact, early experiments indicate that offers matched to the catalog receive up to 40% more user clicks than those that do not and up to 20% conversion’ (sales).
So you should be using GTINs for all your listings, not just for Amazon. This includes your own website and offline sales channels too.