If Proton already has MIDI support out of the box, the next problem is that there may be no sounds to play (at least from what I understand). Basically Windows comes with a file called gm.dls (located in C:/Windows/System32/drivers/) which contains the sounds you hear when you play a MIDI file. I believe Wine (or Linux?) doesn't come with any equivalent (Windows uses Roland's Sound Canvas soundbank).
You might also need DirectMusic (a depreciated component of DirectX, winetricks allows you to install it) but I'm not sure of this and you may in fact not need it.
Nothing extracted yet.
Compatibility Report
System Information
https://gist.github.com/legluondunet/0f0a56fb4e9cb743f111385e554fce69
I confirm:
steam-255940.log
Symptoms
Proton have no midi support or can not activate it
Reproduction
Launch the game and when you arrive at this picture:

you have no music