I know this is a work of fiction because it says there's a song on MTV
It's MTV Japan, they are still running
MTV is "still running" here. But the joke is that Music TeleVision is notorious for never playing any music. in the 80s, you could turn to MTV and it would be running banks of music videos with occasional music industry news and commentary programming. You had a better-than not chance that if you jumped to MTV, you could just, y'know, listen to music.
Over the years, they started including more and more programming that was only tangentially music related, and then eventually not at all music related, until it just became a punchline.
That all said, as I understand it MTV Japan is closer to the original mission statement than MTV is here. They actually still run music programming instead of shitty reality shows.