Skype is catching up to what their users have wanted for years, especially newscasters. The introduction of cloud based video recording across all platforms Long wanted. Very much needed, Skype's decision to introduce this across the board is all part of Microsoft's reimaging what was once the most popular online communications service. Previously video recording was only available on desktop.
Ironically, Windows 10 is not yet ready.
We had video recording with SightSpeed and it was one of the most popular features. That was over 12 years ago and despite Skype following with video after SightSpeed's running start, it eclipsed it and every other play. So while video call recording may not be new, Skype adding it brings a needed feature to their community without any third party services.
The one catch is a thirty day window of keeping the video recording in the chat session. During that time you can download it and save it to local device storage. Perhaps over time Microsoft will offer a subscription to allow for longer storage on the cloud or easy sideloading to OneDrive.