Yeah, but you seem to be assuming that the experience would be completely alien, a language needing to be learned so to speak. I'm not so sure about that, perhaps music being the most visceral of the arts, does not require interpretation or explanation, so that even the unschooled ear can apprehend beauty.
I've no idea if it would be any different for a deaf person to hear music for the first time than for a normal person to hear music, and if it is different I don't know if there is any way to answer "What It's Like for a Deaf Person to Hear Music for the First Time".
My point was that this article really doesn't cover that question, as you said it did.
While it doesn't fully convey the depth of his emotion, or likely even allow us to fully imagine it, I think that looking at the article as a whole, we can see that he basically now can experience music in ways very similar to (and likely the same as) the way we do. He cries to it. He has samples several different kinds of music, and has definite feelings about the genres (e.g., classical vs country). He's actively seeking out new music, and is finding ways to describe (very well, IMO) _why_ he likes one or the other better. He's found a song that he has had to listen to over-and-over.
I think that covers "what it's like" from an emotional perspective very well. It was profoundly moving for me to read this.