There's a pretty vintage feeling to pretty much every aspect of this game that I can appreciate, it's certainly fun and I don't really see anything here that a real Game Boy couldn't really do, though the sound could have been a little more accurate... Good job anyway!
I use Deflemask, it's a multi-system tracker that supports the Game Boy, as well as many other systems like the Mega Drive, the PC engine (my favourite) the Commodore 64 and many others! And Game Boy music made in Deflemask will run in real hardware!
That said though, I realise not everyone likes the Tracker interface, and if that's the case for you I'd suggest using the Nintendo VST by Matt Montag in combination with the Chip32 VST in whatever DAW you like (provided it supports VSTs), you can get fairly accurate GB audio by using 2 square (pulse) channels, 1 wavetable channel (that's what Chip32 is for), and 1 noise channel, but that's only a close enough approximation of GB sound, if you want actual GB sound I don't think there's any options better than Deflemask... Well, some people think LSDJ is better, and it even runs on a real Game Boy, but I personally find it to be very clunky, like, composing music with a D-pad and 4 buttons is anything but ideal...