I did find the article detailing the construction, unfortunately it doesn't have any specific details about the code in the ROM, only a mention that it was created with the help of a Pascal program which does not appear to have been offered. From what I can see, the source file for the EPROM was never offered directly, the author's company would supply either a programmed ROM, a partial kit with the ROM and PCB, or a complete kit with everything, none of which is any help since the company is long gone and I would not be surprised if the author is dead by now.
Yes I'm sure we could work out the "code" to implement a ROM based state machine duplicating the function of the original design given sufficient effort although that could prove to be quite a lot of work and push the effort required to build this one beyond what is reasonably worth doing. I am intrigued by the design though, I have built finite state machines in FPGAs before and but other than in the Atari vector games I can't think of any other places I've encountered one in "real life".