Neville the subject flight was flying an RNAV approach that follows the Canarsie approach and is designed by EK for use by the 380. The reasons for the design are questionable but one is the limition of the 380 FMS. There is a published distance height table that is based on the CRI VOR and covers from ASALT to DMYHL. Beyond that point in addition to visual cues the FMS displays a constant descent flight path which you could have validated on the previous segment from CRI to DMYHL. Using the Position page as suggested is of little use as its assumes a straight line to the threshold. The very same FMS is displaying distance to go via the curved path so why not use that. So a distance to height cross check is used or at least can and should be used on this approach as with any other. But hey I've only ever flown it once..