Bob Blakely is speaking about building a relationship layer for the Internet. A relationship is the context within which we observe one another. Past history and even attitudes are not directly observable. This is imperfect--distant relationships are the basis for inaccuracies. More observations at a closer distance make for a more useful and feature rich relationship.
Bob puts forward the emergence of the credit card industry as an example. Rather than requiring shoppers to create intimate relationships with every merchant, you create a single intimate relationship with your bank and the merchant has an intimate relationship with their bank and then the banks form a relationship (contract) that connects those.
Generalizing this thought to identity, in situations where you don't have one good relationships can two relationships provide the answer? Intermediaries need to have a trust relationship with the user. Phone companies, utilities, even shipping companies have a great advantage here. They can out compete banks.
Relationships are the type information about edges in the social graph. Bob presents a schema for relationships. Relationships have a creator. Relationships have a type (FacebookFriend). Creators establish rules and roles. Rules might be "can't copy." Roles are descriptions of individuals who can participate in the relationship.
There are other elements in the schema. Consents are what you agree to (i.e. enter into a relationship, you can send email, etc.). Promises are things you're held to (i.e. abide by terms of service). You also have claims (i.e. this is my name, this is my email address, etc.) There might be blocks to list other participants. The schema is a contract sorts. In privacy, for example, this shifts the discussion from one of rights to one of contract law.
Employees present an expensive relationship. Contractors are a less expensive way of having an employee relationship. This is relationship federation. The contracting company provides context about the relationship and there are rules, etc. that govern the relationship.
Identity providers present a similar scenario. The IdP can, in theory, create the expensive relationship with the user and with the RP. The difference is that IdPs can't make money from the expensive user relationship. You're not selling identity. If you sell identity, like Equifax, people hate you. You're selling relationships. They should compete on the basis of cost and quality.
"X-centric" is dysfunctional nomenclature no matter what the value of "X." Functional relationships happen when both parties gain value and agree to treat each other with respect.