This add-on actually can *not* save videos. In order to save a video, it asks for downloading a 'companion' app, which is an executable that has to be installed separately and hence the browser security restrictions do not apply to it - it can do virtually anything.
This is highly suspicious, because external applications are not necessary in order to save files. I removed it and installed a different video downloader add-on which can save files just fine without 'companion' executables.
Another suspicious thing is that this addon requires some permissions which are not needed for the functionality it provides.