if you have a sound recording program like soundforge/audacity and a soundcard which has the right hardware/driver…

Look for a a fader marked “stereo mix” on the “recording control” bit on the Windows volume control. This will set your sound recording program to record anything the output of your soundcard is producing

NB: ensure your playback “line in” isn’t active or you will get feedback!

click record a few seconds beforehand (you can edit out the blank bit)

start the youtube content and your sound recording program should record this…