I always have loved this piece; such power and emotion contained in it, especially in the context of the game. Glad to hear it remixed by you. Guess my request pushed you to completing it, huh? :)
While it is not perfect, it is QUITE good, and I think you aren't giving yourself enough credit. My two areas where I feel it was lacking was the phrase at :27. The melody's pitch, while not wrong or dissonant, I wish was higher, to match the same notes as the original, and the harmony loses some of the energy and darkness too. Maybe I'm just being harsh here, but the phrase loses some of the original force.
The other part is the transition from 1:09 to 1:10. I think the key change you made further back left the original's key, which is fine, but then you return to the original's key at 1:10. So it was a bit disconcerting.
Other than that, great work! I know this was a tough one for you. The start and ending of the song have great energy and retain the original's desperation, and while the middle is a bit weaker it still stands strong. I would have liked more percussion but I think that is an 8-bit limitation that you are sticking with, so it's all good. Very enjoyable!