His last sentence mostly. "project planning, reporting, managing expectations, coordinating teams and delivering on time. It's not terribly rewarding or creative work, but it's what MBAs can reliably produce."

Aka stakeholder and expectation management. The above sounds easy but requires a large number of "soft skills" to do well in a large organization.

I think it is a vague idiom by intent, but here's one definition: "To behave in a way that is accepted or demanded by those in authority"(http://idioms.thefreedictionary.com/play+the+game)

I view this skill as anticipating not just what your boss tells you to do, but also the things they don't make explicit, because you recognize subtle social cues and understand their incentives. It can be nefarious or just empathetic. How it is deployed determines the morality of its use, in my consequentialist opinion.

The corporate game.

Wear a suit (or dress appropriately for the situation), turn up to meetings on time with an agenda, manage teams, hit deadlines, send well crafted emails, give feedback, communicate effectively, lead people, turn up everyday and be consistent, grow

Obtaining proper credentialing, networking, being able to work long hours under pressure, and articulating what clients want to hear via impressive power point presentations and spreadsheets.

The game is do good work, get good schooling, perform well taking care of some one else's business and make money. What's the goal? Money through value creation.