Manipulation greases the wheels of Richard III. Richard is constantly manipulating characters around him in an acrobatic performance of subtlety and wordplay. Richard's skill at manipulating everyone around him is key to his success. It also increases our begrudging admiration of him, even though it's pretty clear that he manipulates us, his audience, as well. By letting us in on the secret details of his scheming, he creates an atmosphere of complicity.
Richard's manipulative tactics also keep the play lively, and the skill with which they're executed keep us on his side throughout most of the play. It's like looking inside an incredibly artful machine.
By making the audience members his confidants at the beginning of the play, Richard manipulates us just as he manipulates the characters around him.
Richard is able to manipulate everyone around him because he's a good actor, has strong rhetorical skills, and can think on his feet.