Let me ask you this; if Relogic or Scott Lloyd Shelley (the composer of all of the music in the game) aren't the ones "taking you to court", then who would?
Relogic has never taken legal action that I'm aware of towards a genuine Terraria Youtuber/streamer for copyright infringement of their music. And while Youtube's ToS may indicate these rules, consider also the massive quantity of Terraria videos showing in-game music in them; Relogic employees regularly watch such videos for a variety of reasons, and are well aware of it.
The sort of thing where you might run into trouble is if you were to, for instance, take the Terraria music and use it for other purposes, like playing it over completely non-Terraria videos, using it in other products or media (like a video game), claiming it is your own, or trying to make a profit from it. In terms of showing the game Terraria being played, the music is just another part of that, and there are thousands if not tens of thousands of videos already doing this.
If you like, I can see about getting some official word from above on the matter. But I'd ask you consider this; if thousands of other videos are doing the same with no issue, and Relogic itself is alright with this, what is Youtube going to do to you? They don't have any legal case against you (its not their property to seek legal action on), and this would contradict half a decade worth of precedent in allowing these sorts of videos. Ultimately, its up to you whether you are too concerned with Youtube's rules to use the music, but this is a very established (and even encouraged) practice that is all very above board.