A small figure of a person or animal, having a cloth body and hollow head, designed to be fitted over and manipulated by the hand.
A figure having jointed parts animated from above by strings or wires; a marionette.
A toy representing a human figure; a doll.
One whose behavior is determined by the will of others: a political puppet.
Obviously the 5th definition fits the best description of John Malkovich behaving as a puppet. Throughout the movie his actions and speech has been controlled by someone else. The puppeteer, Craig, has enough mindset to be able to completely control John without John being able to take back control. I think it has more with Craig's desire for Maxine than his skills as a puppeteer that allows him to control Malkovich. I think all the different people that end up in Malkovich's mind represent the different personalities of his self-conscious. It's like he's not ever completely in control of himself. All of the people he wants to be and all of the people he once was are what controls him. He is never acting in the present and now. He is always acting from past and present beings.