As opposed to what some people might think, you really don't have to be a genius to solve the Rubik's cube. It's actually quite easy.
All you have to do is memorize about 50 "moves" each consisting of about 15 cube turns.
Seriously now, there are many systems to solve the cube, and they mainly work by building up the cube (first one side with a T on all the sides next to it, then the middle layer, bottom corners and bottom center pieces). There are also many different ways to build up the cube.
What's interesting though is that the robot does not scan the cube while it's solving it. They must have used a different system or programmed the robot to know the position of all the cube pieces after every move.