Better than trying to add context menu commands to the minimalist Pantheon-Files of Elementary OS or to use other media applications to extract sound from video, I guess the most simple is just to install Nautilus (it is not at all problematic in eOS, contrary to Thunar, which comes with the whole Xfce environment).
sudo apt-get install nautilus
Then install Nautilus-Actions Configuration Tool and open it..
I will provide an example for extracting audio (aac in m4a container) from flv and mp4 video files.
Define a new action, give it a name, maybe an icon too. Check - 'Display action in selection context menu'.

Under the command tab, add the command
bash -c 'ffmpeg -i "$0" -map 0:1 -c:a copy "${0%%.*}".m4a' %f
.

Under Execution tab there are options to select depending on what you want to see during and after the action (open terminal, report).
Under Mimetypes tab, enter the filters for the type of files in the context menu of which you want to see the command - in this case: video/mp4
and video/flv
.

There are other options, but these look sufficient for the purpose of my question.

Similar actions can be added to extract sound from other types of video and, of course, for other very different purposes.
(This solution is based on suggestions and solutions present in the links already posted in the question and the credit goes to the authors.)
Can be used in Thunar custom actions too.
My initial source is this.