The methodology deepmind used for training the game player is based on a classical reinforcement learning algorithm called Q Learning (http://en.wikipedia.org/wiki/Q-learning), developed in the late 1980's. This approach of maximizing expected future rewards for the agent to select an action in a current state has some parallels with studies of how the basal ganglia region of our brain conduct reward learning (basal ganglia).
What has been done is to approximate the reward function Q (which originally used a look up table) by a more general function to approach larger problems with much larger (or infinite) number of states. The approach here was to use a function which can fit large amounts of data, in this case a multi layered neural network (with convnet layers to preprocess the raw image input first to identify features) to attempt to learn the game.
This has actually been done a while ago, by Tesauro (now at IBM research) who used the same approach to create a Q Learning agent to play Back Gammon at an advanced level.
The reason why this is new is because in recent years we can employ cheap GPU's to learn exponentially more quicker than conventional cpu's and can construct much larger and deeper networks to learn from more complicated systems. Also many new 'tricks' have been developed to optimize learning in recent years (sigmoid functions replaced by simplified rect linear function, and dropout, etc), so we are going to see better and more amazing uses for this relatively old technology.