The quoted Mach 0.96 / 654mph number will be a true airspeed, i.e. speed relative to the surrounding air (which may itself be moving)
The speeds in the FA graph/tracklog you see are groundspeeds, i.e. speed relative to the Earth’s surface, which includes the effect of any head- or tail-wind.
For this particular flight, the reported TAS [true airspeed] at the time was around 500kt = 575mph, so there was a tailwind component of around ~80mph
The ground speed you see on flight trackers includes the effect of tailwinds, so it isn’t the aircraft’s true airspeed. An A380 can show unusually high ground speeds when riding a strong jet stream, especially on eastbound flights to Dubai. So it’s very unlikely this was a world speed record for the aircraft itself—it was most likely a combination of normal cruise speed and exceptionally favorable winds.