Intercept request or console output on a public server?

Hello, I use a website (Streamlabs) that allows people to send a Youtube video played on a web page embedding the Youtube video player (https://www.streamlabs.com/widgets/media/v1/my-secret-key).​With Node, I'd like to save all videos send to watch them later, but it looks like the Streamlabs API don't provide this information yet. Is it possible to do it myself considering when I open the devtools:- In the network tab, I see the GET request to Youtube when the video is played (the video ID is in the request URL),- In the console tab, I see an output containing all necessary data.- They are using the Youtube Iframe API, not the