Are these songs actually used in the TV series?
Nope.
Literary Song Videos. They come in 2 types - living room videos and auditorium videos.
Take the lyrics of a song as, essentially, a short story. Then illustrate them in a video context. Exactly the same internal structures as a short story.
For an auditorium video, almost all the clips chosen are matches of actions to words so that everyone can “get it”. For a living room video, you pile complexity upon complexity so that the more you get to know the show, the more subtlety you’ll find in the 3 short minutes. Think of it as a mental game and it will make more sense.
Almost NO connection to what is a traditional MTV video.