I'm working on the Battleship you sent. Unfortunately, there's a little chip out of the TMS1000 die, over part of the O output PLA frown Those outputs are connected to the SN76477 mad I recorded sounds while playing the game, so hopefully we can figure out the missing bits.

Here's a short video:

I count 6 different sounds: high and low tones used for player input feedback, sonar ping, bomb falling, explosion, and klaxon.

I couldn't find any die shots of the SN76477, so I decapped it: