Na verdade: não, não há uma maneira conhecida de reproduzi-los diretamente no navegador em um mac. Pode haver a possibilidade de reproduzi-lo em um sistema Linux em um navegador como o firefox com wrappers. Existe um bom tópico no reddit que analisou este problema:
While MIDI is a relatively well defined format, it does not define how the music should be played. On old sound cards there was an FM chip that generated the synthetic sounds we all know and love. On Linux, you can use Timidity+ together with a soundfont to play sounds of a much higher quality, but at the cost of CPU and memory usage. Some people just wants to hear some blips while others want the Cello to actually sound like a Cello and route it through their robotic Cello player that they have in their livingroom, and the rest through their hand crafted external analog synth module. In short: it's hard for browser developers to come up with a way of generating the sounds in a way that everyone will accept. In my opinion, something sounding like FM generated sounds should be the default, instead of just silence.
On Linux, it's relatively easy to play MIDI files with Timidity+ or a front end like KMIDI. I'm not entirely sure, but I think KMIDI or one of the other media player frontends can both be embedded and play midi files. I bet ffmpeg can do it. I assume you're using a Linux distribution, since it's not mentioned in the text.
A única maneira conhecida de reproduzir os arquivos MIDI é baixar os arquivos e reproduzi-los com um player local como vlc.