I just typed in "Neil Cicierega Aerolong" into the YouTube web search bar and what you were looking for is the first thing that comes up, just the isolated video with that track.
Interestingly, on music.youtube.com, only the fan extended version and an unofficial video come up, not the plain track that shows up on normal full YouTube.
Home Mini used to search YouTube first. At some point, they changed the preferred context to Play Music, and you would have to say, "Play x on YouTube" to get YouTube audio, even if a more correct result was on YouTube than was on Play Music. Obviously, Play Music is no longer available; it seems like it it now completely ignores YouTube searches and will only use YouTube Music.
Interestingly, on music.youtube.com, only the fan extended version and an unofficial video come up, not the plain track that shows up on normal full YouTube.
Which of those does the Google Home Mini search?