In the 1980's I can remember seeing a computer chess board that had a robot arm to move the pieces. It was even featured on television, playing against Shane Hill (IIRC). But it was a bit of a fad, and soon the whole "self moving" chess board went away.
However it isn't entirely dead, as a new design group is developing a slightly more aesthetic board, using magnets under the board, rather than a more obtrusive robot arm. There is even a kickstarter campaign to support it, and at the time of writing they are two thirds of the way to their goal.
The product is called "Square Off" and it is a normal chess board, except it can move the pieces itself, using a 2-axis robotic arm with a magnetic head, so it can slide the pieces around the board. It is controlled by a phone app and has extra features to enable live broadcasting of games.
Of course such boards aren't exactly cheap, although the base model is 200 euros (for early purchasers) which is cheaper than a DGT board.
I'm not sure if I will ever shell out for one, but as someone who used to work in robotics, it seems like a smart approach to an old problem.