Does artificial intelligence run the planet?

No. Artificial Intelligence is far too primitive to do that. Human intelligence, often using sophisticated software tools that only seem intelligent, runs the planet. That "seem intelligent" is the key; AI is the new Philosopher's Stone, the eternally unobtainable Holy Grail.

However, the argument could be made that artificial people do run the planet or more accurately many little parts of the planet. Tune in to a couple hors of CSPAN and you'll see what I mean by artificial people.