Identity is a somewhat philosophical and thus nebulous concept.
What is my 'real identity', honestly? How does a bank prevent me from opening an account in the name of my hypothetical identical twin if I borrow the appropriate documents? How would a government agency?
The reality is that identity winds up being evaluated as a relationship. My bank identity is as a particular customer, and me attempting to opening an account in someone else's name doesn't change that - rather, it is a sign I as a customer am planning to commit fraud. In some fashion, a process attempting to tie an interaction to an identity is actually attempting to tie behavior to consequences.
This made the article a bit difficult to understand - was the point that the sharing of identity, and thus trying to die back to one 'true/real identity', is flawed?
Or perhaps that this concept of local identity isn't always needed to perform a transaction - I don't care who a customer is as long as I know the information that I'm acting on is true?
Single Sign-on itself is an often abused topic - it generally means that authentication (providing proof that you correspond to a particular identity I hold) is reused.
However, Federation is the process of sharing that information across domains, and is usually done via protocols like OpenID Connect or SAML.
Google Sign-In, Facebook Connect, and other IDPs usually combine both - and the value comes not from signing in with google credentials, but that you often already are signed in with google/etc credentials.
The value you get back contains a subject attribute, which is a unique (possibly globally, or perhaps only within your service) identifier for the user account upstream. This value is what turns these social logins to an authentication for your own site or app.
At the minimal level, the information leakage is mostly to the IDP - they see where and when you are authenticating. However, the IDP is free to offer whatever additional attributes and authorizations they decide to - verified email addresses, API access to user data, and so on.
Possibly, the IDP even shares some piece of information your service might rely upon because you consider it the user's 'real' identity.