In MacOS recording System audio from "Your Entire Screen" or "Application Window" is not supported. This is a fundamental limitation of MacOS, for security reason the operating system doesn’t allow the browser to access the entire system audio.

However you can always record the Audio from a Tab when choosing "Chrome Tab" instead.

Steps

Open Screen Recorder - Scre.io
Select "Screen Only"
Select "System + Mic." or "System"
Click "Start Recording"

Switch to "Chrome Tab"
Select the Tab you want to record
Make sure "Share audio" is selected
Share

Updated on: 08 / 03 / 2021