If you're looking at the "how" specifically:
This would play MIDI files, not MP3s. Midi files are the digital version of that book with the punched holes, it's a sequence of note events over time.
The physical book with holes forms a series of air valves. So what you do to convert it is attach a bunch of pneumatic solenoid valves instead. Then there is some interface board that lets you control a bunch of solenoids from a laptop. It's not really that complicated but you need one valve for each note, so you need a lot of them, and you have to physically plumb in each one to the organ.
Have a look at Look Mum No Computer, he does this kind of stuff: https://www.lookmumnocomputer.com/projects#/joans-church-org...
Very cool, this is exactly what I was looking for to answer the how question.
These projects look awesome, if I'm ever in the UK I'll checkout their museum.