OK, so just a simple 2 channel pre-programmed AWG.
The "signal select" slide switch would set the upper bits of the address bus (either direct to EEPROM or loaded into the upper ls161 counter), and the counters get clocked by the reference input.
Different EPROMs would allow synthesis of different demo waveforms, which explains the dodgy looking labeling.
Out of interest, how is the box powered?
Maybe you could capture the analog output waveforms for "posterity".