Thank you JeremyMTC....interesting results....
I contacted the person listed on the website. His son replied back to me. Sadly, his father (the man who designed and built the board) passed away in 2011. He did recognize it, and was able to tell me what it was - it was part of an arcade-wide tracking system:
"My father's Money Tracking System worked as follows: let's say an arcade was filled with 50 games of all different types (like video games, crane games, etc.). You would install a remote board in each game, like the one you have in your machine, and connect it to the coin switch. If you look at the remote board, you'll see 2 "phone" type jacks marked "In" and "Out". You would use those jacks to connect all of the 50 machines together, and then to a "Master", or "Main" unit, almost like a network you would see today. Each remote board had it's own unique number to identify it on the network. The main unit was usually back in the office, or somewhere similar. This allowed the owners of the arcade to track, and record, at a glance exactly how much money each game was taking in, and how much money was being made overall."
Interesting, but of no use to me. If anyone would like it, let me know.