There are chess boards with self moving pieces out there. Some use a robotic arm under the board with a magnet to move pieces. [0]
I ran across a board that claims no moving parts for moving pieces, but couldn't find a description of how it accomplished that. I am guessing some sort of coil configuration under the board inducing a magnetic field to move the pieces, but I really don't know. [1]
https://www.youtube.com/watch?v=mb-jmHT6Xz4&t=36s