The ORDER hasn't changed, just the value.
This adjustment allows for a more accurate calculation of an elements mass, but it does not alter the fundamental position of an element in the Periodic Table. The original values were also based on relative mass. The refinement of the isotopic distribution contribution does not significantly change an elements mass relative to the other elements.
More importantly, the significance of the Periodic Table is not for a mass listing, but for the arrangement in columns of elements with similar electronic configurations, and therefore, properties. The rows show the "build up" of the elements and how the addition of protons and electrons change the chemical properties.