Theoretically, anything that can implement boolean logic can be used to build a Turing-complete CPU. It just needs to represent a "true" state", a "false" state, a way to make a comparisons, and an input and output mechanism to feed other subunits or retrieve data from them. Stuff like this has also been implemented using water pumps/valves, and even in Minecraft using redstone. Computers don't have to be based on electronics.