As Twitter, Amazon and etc... uses T.co, A.co respectively uses their own URL shorteners, Google too has come up with its own URL shortener service with G.co. Google still has goo.gl URL shortener service but it is for public use.
G.co is only for official use. Only the websites which will be owned by Google will have these links. G.co will not be available for public service. This service will help the users to clearly know which is an unofficial site and which is official site of Google.
