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.