According to the latest (Dec 2015) documentation for Webex Operating System and Browser Support, in footnote 2 they say:
Linux is not supported for Personal Rooms.
You may not give up all hope, as footnote 3 says Firefox 64-bit is not supported, which is not accurate as I use 64-bit Firefox with 64-bit Java 7.x (Oracle JDK) by manually symlinking libnpjp2.so
to /usr/lib/mozilla/plugins/
.
But now with MacOS not using Java and using a plugin instead (footnote 1), it seems unlikely to use Webex Personal Rooms on Linux, unless they release a plugin for us.