I listened to the original before this just so I had some sort of reference, and I must say this is a really awesome take on the original. I really like the difference in mood compared to the original just by using a piano.
Before the change midway (in..key? Not really sure what the term is), I feel like it could have taken off on another direction and made a story on it's own, but I guess you would've wanted to stay faithful to the original, which is fine. It was just something that I noticed while listening.
Anyway, really enjoyable listen, I feel like as someone who hasn't played the game, I could probably write a story just based on what I'm listening to here. I don't stumble across songs like that often so yeah, good job :p. Keep it up!