Приведу цитату из инструкции на английском. Проверил, этот способ работает.
To reach the direct video and audio links: (using Chrome)
- Navigate to the desired youtube video.
- Press F12 to open Chrome DevTools, and then select the ‘Network’ tab.
- Ensure network recording log is turned on, indicated by the red circle near the top-left. To enable, press the black circle or press ‘Ctrl-E’.
- In the filter box, search for ‘mime=video’. If you just turned on network recording you may to press ‘F5’ to refresh in order to see results.
- Right click on the entry nearest the bottom and select ‘Open in new tab’.
- In the new tab, you’ll be faced with a empty media player that doesn’t work. The URL is very long, and you will need to modify it slightly to allow the video to play. Near the end of the URL you will find a ‘range’ parameter similar to this: &range=15880614-17942602
- Remove this section of the URL and renavigate to the URL.
- You now have a direct video download link. You can view the video from this URL or right-click on the video frame to download locally.
- Repeat from step 4 using ‘mime=audio’ in the filter to download the audio.