Allow me to clarify and elaborate on using Audacity. Any youtube video can be recorded using Audacity; Audacity does not care about copyrights or whether recording a video is blocked by the publisher. The reason is that Audacity is simply recording anything it hears, including any sound coming from the speakers. Keep in mind that recording with Audacity requires a mic connected to the computer. Most laptops have a built-in mic. With most desktop systems, the typical hardware configuration for this type of recording requires the addition of an external mic, such as a USB webcam.
I tested this on a desktop system with a USB webcam mounted on top of my monitor. I recorded a video but, since the mic in my webcam will not record stereo sound, the outcome, i.e, the recording, lacks stereo sound. Also, since my speakers were sitting below, and slightly behind, my monitor, and, again, the webcam was sitting on top of the monitor, this was not the best configuration of speakers and webcam to capture sound from the speakers. If I wanted to do more recording from any web source, I would rearrange the speakers and/or webcam so that they are facing each other rather than being faced the same direction.