I haven't used this extension before but it seems like what it does is find the URLs of active videos. You can do the same manually by F9(or right click > inspect) > Network > Media > Sort by size (larger files will probably be video). This will give you the URL of the video (same as if you right clicked and chose "open video in new tab", but some sites disable this).

This approach usually works for me, but many sites take steps to prevent it.

1. Send several smaller video files. They basically cut it up into short videos so you can't access the whole thing at once. ffmpeg or a download manager (I use TurboDownloadManager) should be able to combine them relatively easily. Until recently, YouTube used this sort of method. The URL had a "range" tag that specified which frames of the video to show. Deleting this tag gave the whole video. They've since changed it and I don't know any similar tricks (just use yt-dlp for YouTube). Other sites may do something similar, like changing a number or keyword in the URL will get you the whole video.

2. Serve a preview of a full video (that you have to pay for). Many sites have very similar URLs for free and paid videos. On some sites you might be able to guess what you need to change to get the full video. Some sites have their previews named "preview.mp4" whee the full vudeo is the same URL but named "video.mp4" or something like that. You can spend some time messing around if you find something like this, but really the chances of guessing correctly are pretty low.

3. Encrypted keys. This is basically impossible to crack. Some URLs will have long strings of letters and numbers in them. I assume this is some sort of encrypted password that needs to match up for you to access the video. Don't even try with these ones.

TL;DR usually it'll work. Sometimes it won't but you might be able to get around it.

Also, yt-dlp works on much more than just YouTube. If I can't figure out how to download a video, I'll just give the URL (the webpage, not the direct video URL) to yt-dlp and it'll often work.

I don't know what method it uses for streaming content, if it's HLS I don't see why it wouldn't work.