Who is Mr. Gold in the movie Revolver?

The movie isn't an analogy to chess. The movie is about the illusion that imprisons every one of us.

Deep beneath the films violence, blood and grit, lurks a spiritual and enlightening message - a message echoed throughout time by revered figures such as Buddha and Bodhidharma, a message also echoed in Kabbalah (which is probably where Guy Ritchie drew his inspiration from, as his then-wife, Madonna, is heavily into Kabbalah). And that message is this: we are not our ego; the ego, far from being our friend, is responsible for most of our pain and misery; the ego is a product of the mind and creates the illusion of separation, the ego is a prison, a prison that very few people recognise as such.

To answer your question: Mr. Gold is everyone's ego. In Jake's case, Mr. Gold is the part of Jake who wants to kill Macha.