Some people can just turn everything on like you did and everything works. That’s how Chase did it on his webcast Reel Life.
http://reellife.podomatic.com/
If that didn’t work for you, then you need one of the third party software programs or services. Audacity is not recommended for recording both sides of Skype.
https://forum.audacityteam.org/t/how-to-record-audio-from-skype/46575/1
https://forum.audacityteam.org/t/recording-skype-settings-help/46936/1
The list so far:
Record Skype
Pamela
Recordator
Voicemeeter Banana
Spreaker
Two Computers and Small Mixer.
Standalone Recorder sitting on the table.
If you get a different process to work, post back and we’ll add it to the list.
Koz