I know where you can find the identity of the game. It would be very helpful if you remembered the game developer. Was it Taito, Data East, Sega, Irem Corp., Konami, Leland Corp., and so forth.
Here's the website. You will be quite surprised how many games have been developed by your favorite arcade manufactures that you never saw the light of day.
Awesome website! It tells you all about the hardware involved with arcade technology.
Just a little F.Y.I. In 1988, Sega Y-Boards, while technically just 16-bit systems, were already pushing the output of later 32-bit systems. Arcade technology was about 10-15 years more advanced than the home consumer systems.