Unfortunately it seems that you can only do it that way, even when the deeper information gives a clue on which browsers you can use, it also gives null expectations about its usage under linux, as we can read in: http://www.facebook.com/help/?faq=211644178877843
Which browser should I use to set up
== Video calling works best with the latest versions of the following
Note that video calling for Linux is not currently supported. You will
need to use one of these browsers in a
Mac or Windows operating system. If
you’re having trouble with video
calling, try upgrading or switching
your browser using the links above.
Nevertheless, the sentence that reads "is not currently supported" gives a hope that they will work on such a support for linux users, so let's wait patiently for it.
Anyway, in my personal experience using internet explorer under wine, I didn't get native results as in a MS based system, so you may experience some issues when trying to use this feature.
Please inform if you succeeded, it would be really useful to know if you could have at least a communication through this system.
Thanks in advance and Good luck!