"The synthesizer is implemented on an ATmega88, an 8-bit microcontroller with 1 kB of RAM and 8.5 kB of ROM. It receives MIDI data at a jumper-configurable baud rate and produces a 12-bit mono line out signal. What follows is a brief architectural overview."
Is a very very smart programmer and I bet that everything is done using assembly, and it doesnt have a lot of interrupts firing so you can have nice things like millis, or serial comms.
But add some extra code to take advantage of those high frequency PWM outputs. The ATtiny45 has 2 High Frequency PWM outputs, which could generate 16-bit High Quality output from the other page above. Just need to figure out the whole thing first.