How I do it:
1, Open the network inspector tool in your browser (f12 on Firefox which is what I use).
2,Refresh the page so it starts monitoring.
3,Play the video and watch for new urls or data transfer size increases.
4,Sort by highest amount of data transferred.
5,Usually media files/streams are the largest value but search for a known video file type. Sometimes they will be temporary streams that are .rtmp's or similar if not videos.
6,Open the url that matches all the above in a new tab and save as normal.
This is all basically every media ripping plugin/app/tool does.