Virtualdesktop.org seems to just be a collection of images for each OS as far as I can see. If you click an icon in the OS (which is just a normal hyperlink) it just opens the image that contains a screenshot of that application. There doesn't seem to be any actual virtualisation there.
It wouldn't be a major task to create something similar by using bhyve as a backend. You'd just need some way to clone a pre-made OS/bhyve image (easy if stored on a ZFS dataset) & boot it wih bhyve, then connect to it from a browser based VNC client. I wouldn't recommend doing something like this and making it public on the Internet though..
Also note that FreeNAS 10 (which I think you can get the beta for at the moment) has bhyve support, including VNC access via the FreeNAS web administration. Of course the web interface is intended for administration, not for providing web based virtualisation to third-parties. (I think the same generally applies for ClonOS)
A browser-based VNC Client should be the best solution. NoVNC is currently adapted nearly everywhere, as it is HTML5-based and not dependent to any java runtime like most other solutions (which tend to break on every second jre-update after full moon).
ClonOS also uses NoVNC as it seems from looking at their github repository