Here's a video about how player pianos work:

https://www.youtube.com/watch?v=2GcmGyhc-IA

Basically, you have some pedals which generate a vacuum, and then everything is powered and controlled via vacuum. (The internet may not be a series of tubes, but a player piano literally is.)

Using vacuum to control things may seem very niche and exotic, but it was actually very common. Basically every car engine up through about the 1980s used vacuum to control the engine. Cars with a mechanical ignition system often used a vacuum advance to adjust the timing at higher RPMs, for example. Early cruise control systems used vacuum to adjust the throttle.

Anyway, all pianos have felt hammers which strike the string. When you're playing the piano manually, there's a mechanical linkage between the key you press and its hammer. In a player piano, there's another way to move the hammer: a vacuum controlled actuator. The piano roll has holes in it corresponding to notes. The holes allow air to pass through, and that causes the actuator to push the hammer into the string.

In that dance hall machine, which appears to be essentially a pipe organ, there are some similarities and some differences. A pipe organ works by blowing air through the pipes. There's a "wind chest" that stores pressurized air, and when you press a key on the keyboard, it opens a valve to let air into a particular pipe. In the old days, that linkage (between the key and the valve) was mechanical. These days it's electrical or electronic.

At the end of the video above, he even briefly mentions a band organ (which is similar to a dance hall machine) and how music rolls work for it, and it's a similar vacuum system to a player piano.

So I believe a dance hall machine with a music roll probably uses a combination of vacuum and positive pressure. The vacuum would allow reading the music roll (the paper with holes in it corresponding to notes), and that vacuum would actuate valves that allow positive pressure air into the pipes to make sound. In order to convert one of those to be controlled electronically, you could use a bunch of solenoid valves to either control the vacuum or directly control the air going into the pipes. I'm not sure which way they do it.