The earth transformed into ... "The Cursed Earth"
Mr Pedantic here.. I'm looking at a freeze-frame of the 1995 movie, whose intro reads:
In the third millennium, the world changed. Climate. Nations. All were in upheaval... the earth transformed into a poisonous scorched desert, known as "the Cursed Earth".
So the first movie used rather ambiguous wording which could refer to the planet Earth, or since the text above lacks a capital E on Earth, simply that some earth became scorched and it was called 'the Cursed Earth'.
For the new movie, one could argue that "on Cursed Earth" is dramatic wording implying that events transpire on earth which is considered cursed, and is not necessarily referring to the entire planet or even a region that we fans know as "_the_ Cursed Earth", i.e. that area of nuclear wasteland occupying much of what is currently mainland USA.
I, for one, welcome the new retelling of the old favourite, and will be grateful for what we get. My memories shall remain unsullied.