You only need a webcam to record video, but you may see this anyway. It is just a generic warning message to cover both recorders of video and audio. But you do need to grant access to the microphone.
There was probably a little permissions dialog that you dismissed when you first loaded the page, without realizing the importance of. But you can still do it.This is the toolbar on Chrome when permission has been granted ...
Note the little video camera mark. It might be a microphone in some cases , but in Google Chrome at least you should see a mark there on a page with a recorder.This is how it looks when permission has not been granted.
You can rectify this by clicking on the mark. You should then be able to grant permission to the browser to access the microphone.