There obviously is a demand for a byond version that can play games on Linux. Using third-party software like Wine to render a windows version of Byond is unreliable and shaky at best. There should be an installer for a version of Byond that is linux that is dedicated to running games from the hub.
Linux does have hosting software, but I can agree that running BYOND on Wine is really fragile and usually doesn't work as intended.

The Webclient was supposed to work around this but since the webclient has been on the backburner for some time, it's safe to say that Linux support is currently on the backburner as well since the webclient has a higher priority. However, if the webclient DOES happen to get up to speed, playing games on Linux using your browser would be very doable.
Hm, As of now the Web Client is not terribly reliable either. Some icons won't load, and it's just slower than the native Byond. But, eventually, I suppose it will be good enough to rival the native client and I will be able to play byond games on my Linux os.