Although it was mentioned in the end credits of the movie that there would be an official soundtrack released on EMI, the only official release was the Queen album "A Kind of Magic", which had six songs from the movie in slightly different versions. There is no official release yet, because the rights now with Universal, who have no interest in releasing the score. We have checked with them.
To date, there is no release of the Queen songs as they actually appear in the movie, including their version of "New York, New York".
Update: The 2011 Queen box set has the film version of "A Kind of Magic" on the bonus CD of the eponymous AKOM album as heard over the end credits.