Installed it in Google Chrome, tried downloading a video.
First it didn't work.
Then I tried changing "http" to "https" in the address field of the browser (the Facebook address of the video) and load the page again with the new address. Then I got the two download links ("Download High Quality and "Download Low Quality").
When I clicked the links, the video just showed in Chrome.
I had to right click the download link and select "Save link as" (or something like that, my Chrome speaks Danish). And then it worked - the video downloaded fine as an mp4 file and it was playable.