Chess Game Software
No, there isn't a Windows based application for playing on Chess.com; it is browser based only.
You have a link to the video?
Yes I do have it. It is https://youtu.be/Ao9iOeK_jvU
No, I don't think so. It was computer software. I am software professional, I could make out that its computer software.
Thanks for having look at video and responding.
It's his screen recording software. My guess is he used OBS. One of the more popular options.
OBS has options to crop out parts of your screen and set backgrounds on them. It won't look exactly like that on his computer though.
https://obsproject.com/forum/threads/solved-capture-part-of-a-window.43644/