Here is my list of potential Chess playing Turk arms:
Lynxmotion AL5D 26cm "median reach" (whatever that means), $340
EZ-Robot 6 Servo Arm 50cm "total length"(not much info), $140
OWI-535 Arm 32cm "horizontal reach" (needs feedback system), $45
Dagu 6DOF Arm 39cm length, $275
Trossen PhantomX Pincher 28cm horizontal reach (powerful AX-12A Dyamixel actuators), $400
Trossen PhantomX Reactor 38cm horizontal reach (has a serious reach spec sheet, that shows it really can only reach out 30cm with a vertical pick-up), $550.
Then there is the 5DOF laser-cut DIY arm (requires about $40 of servos).
Some of these could be altered to provide longer reach. A typical chessboard is 12-18 inches (30cm to 46cm), although I did find this 10.5-inch (26.7cm)board as well as this 11-inch (28cm) set. There is a 5-inch (12.7cm) set but I am concerned that positioning to a 0.5-inch square might be tough, plus I may have to remove the magnets from the pieces in this magnetic set. This affordable 7.5-inch (19cm) set may be a good compromise between being small and not being insanely small.
Update: Here is a Lynxmotion AL5C playing chess...OK, I bet an AL5D could do it as well!