While the Robot Store has a wide range of products including robots, not everything here is a robot or robotics. Technically, a robot is not something controlled remotely by a human. Popularly the term is often so applied, as in "robotic" surgery. By that definition, however, Maelzel's chess player would have indeed been a robot when it was actually a midget hidden inside the box making the "machine's" moves. Here's Webster's definition:

1 a : a machine that looks like a human being and performs various complex acts (as walking or talking) of a human being; also : a similar but fictional machine whose lack of capacity for human emotions is often emphasized b : an efficient insensitive person who functions automatically
2 : a device that automatically performs complicated often repetitive tasks
3 : a mechanism guided by automatic controls

A synonym would be "automaton."