I don't think there needs to be any analog. It is similar to, but simpler than, Simon. Just a state machine that gets inputs from the pieces, and some of the states output square waves for the tones.
The SMC databooks on bitsavers talk about their custom chip offerings: http://www.mirrorservice.org/sites/www.bitsavers.org/pdf/standardMicrosystems/
The info changes from year to year, but one year they mentioned that custom work was about 1/3 of their revenue. And they mention the different industries that used their custom chips, including entertainment and toys.
They moved into networking chips and got bought by Microchip a few years ago.
After I clean up the die, I'll post the pics.