download the file and use:
sudo dpkg --install chromium-codecs-ffmpeg-extra_61.0.3163.100-0ubuntu0.16.04.1306_amd64.deb
to install it, or double click on the file. Afterwards completely restart Opera.
This worked without fail. Phew. Perfect stop-gap measure for now. Thanks @xezolitharon !
But this remains to be an issue. I understand and appreciate the troubles with licensing, I really do.
But back to reality: Video's don't work with up to date software, codecs and drivers. No matter the reason, however valid; this is a big problem for Opera. This will drive people to other browsers. Not many people will go to a different browser just for media consumption.
What can we, as a community, do to help move to an actual solution?