Wow, that certainly does sound interesting. :) You may have already known this but the original PONG game featured no central microprocessor and therefore was similar.
Here's some references I found that *Might* help :
"Design of a Tit-Tat-Toe Machine" by R. Haufe in Electrical Engineering, Volume 68, page 885, October 1949
"Relay Moe Plays Tick Tack Toe" by Edmund C. Berkeley in Radio-Electronics, December 1956
Electronic Tick-Tack-Toe in a Cigarette Box" by B. Bawer and W. J. Hawkins in Popular Science 197, pages 78-79, December 1970
Keep in mind that I have read none of these, but they sound like what you are looking for. —hartnell