Thanks! :)
Kohai says not. (See downloading or videos7).
I asked this a while ago, and got the answer from the staff that the vids is not for download.
But I would like to be able to download vids for sure.
What you can do is open them when you have an internet connection, wait for the, to stream and watch them later.
Allowing video download = boosting piracy and violating copyright laws
Thanks guys 
Actually, some downloader online can helps you to download videos.
You may find some useful from this downloader list: http://www.videoconverterfactory.com/tips/best-sites-to-download-videos.html. Just click the right mouse button to display the video. url and copy and paste it on the downloder, you may keep those videos offline. I know catchvideo does a really good job. And it's ok for persoal fair use.
The best & easy way to download chess.com videos online without a downloader software or shady websites that have endless popups is the following :
1. Click F12 on your keyboard & you should see chrome developer tools
2. On the top bar of the tool click "Network" & filter by "Media"
3. Refresh The page & you should see on the left Window called "Name" all the media assets where you will find the MP4 format of the video you want to download, for the example below in the image I have for the scotch opening, the name of the media file hosted on the server is "ENG-OPN-Scotch-y7x.mp4". Now, Right Click & Copy URL
4. Now Open the URL on a new tab & the video should play automatically, on the right bottom corner you will find 3 Dots, Click on it & choose "Download", a window should appear to save the file in your computer, choose your preferred directory & click save .
The best & easy way to download chess.com videos online without a downloader software or shady websites that have endless popups is the following :
1. Click F12 on your keyboard & you should see chrome developer tools
2. On the top bar of the tool click "Network" & filter by "Media"
3. Refresh The page & you should see on the left Window called "Name" all the media assets where you will find the MP4 format of the video you want to download, for the example below in the image I have for the scotch opening download videos, the name of the media file hosted on the server is "ENG-OPN-Scotch-y7x.mp4". Now, Right Click & Copy URL
4. Now Open the URL on a new tab & the video should play automatically, on the right bottom corner you will find 3 Dots, Click on it & choose "Download", a window should appear to save the file in your computer, choose your preferred directory & click save .
I am currently using a Windows application in order to download video from play services like SVTplay and others.
I would rather like to be able to let the Pi itself download the mp4 file to its disk than processing it on Windows first.
Is that possible? I know that the Windows application uses ffmpeg in the background but I have no idea how it is done.
The best solution would be to have a command line interface (so I can do it while remotely logged on via SSH) and supply an URL to some function that finds the stream on the page and downloads it.
Maybe there are already Debian programs that can do this and can be run on a Pi?
As a diamond member, I get full access to the chess.com video library. Is it possible for me to download some of the videos, so I could watch them when I do not have access to the internet (or is this not allowed)?
Thanks! :)