In the hope that someone might have encountered that already and
possibly know a solution:

When I'm trying to join a WebEx meeting from my desktop computer, I get
a working camera display the preview (possibly no audio, though). When
trying to join an actual meeting, a "spinning something" appears for a
short while and then, the error message

Your browser doesn't meet Webex system requirements. Install and
activate the OpenH264 Video Codec provided by Cisco Systems, Inc. and
then try joining again.

gets displayed. Both the codec and 'Cisco WebEx Extension' are installed
and activated, though.