Does the Gamebuino support midi or chiptune music?

Play midi files with the speaker or to use a Midi device with it?

Playing it with the built in speaker. 

You could convert them to an 8-bit unsigned single-channel wav file and play that back.

Or, you could write your own sound handler! How to do that you could check stuff from the arduboy crosscompilation: https://github.com/Sorunome/Gamebuino-ArduboyPlaytune/blob/master/src/Gamebuino-ArduboyPlaytune.cpp#L102

When you convert it to a wave file, you can use my player ;).

https://gamebuino.com/creations/wavplayer

Of course it'd be possible to add.  Just write a software mixer and then plug it into the Gamebuino's sound output.  You could probably even borrow the most popular library for Arduboy but you'd have to rewrite the actual channel volume mixing component in C (since it's written in optimized assembler IIRC).  Shouldn't be a hard thing to do though.

You could probably even borrow the most popular library for Arduboy but you'd have to rewrite the actual channel volume mixing component in C (since it's written in optimized assembler IIRC).

do you mean this? xP https://github.com/Sorunome/Gamebuino-ArduboyPlaytune

There's more stuff in the arduboy crosscompile https://gamebuino.com/creations/arduboy-crosscompiling

Nope, was referring to the chiptune stuff that TeamARG was working on... ATMLib I think or something like that.