Currently, it sees a board of 3x3 states, as in:

_ _ G

G B B

_ _ G

A next step would be to use real computer vision over a 3D camera in the environment aligned to R2D@ and a deep neural network to interpret pixels instead of states. DeepMind has a paper describing this approach: http://arxiv.org/pdf/1312.5602.pdf

It seems like board is kept as a grid and merely represented with three.js; look into the page's source and you'll see a GameBoard object as well as its logic.