The Warhammer Fantasy world is not Earth, if by that we mean it is the past or future of a world with a recorded history essentially identical to our own.
Warhammer has countries with cultures highly similar to countries in our world. This is actually a point against it being Earth, since it is rather improbable that, for example, a country rather similar to Austria would arise twice in essentially the same way. Fantasy counterpart cultures of Warhammer Fantasy include:
The Empire bears obvious similarities to Austria, Germany, and the Austro-Hungarian Empire. Naming schemes are fairly obviously German-derived. The Empire has former provinces such as Drakwald (basically the German Drachenwald). People have German names everywhere you look.
Nippon is literally "Japan" in Japanese.
Cathay is an old word for China.
Albion is the old name of Britain
But the events that occur in the novels and games could not have taken place when those names and cultures were in currency in our world. The entire game is also set at a Renaissance level of technology, but history has no record of dwarves, elves, or vampires living in Renaissance Europe, nor the worship of Chaos Gods.
Another thing, which precludes Warhammer Fantasy being set in the past of Earth, is the End Times, which resulted in the Age of Sigmar. Basically, the entire Warhammer Fantasy world was completely destroyed:
Following the destruction of the Warhammer World by the forces of
Chaos, Sigmar floated through outer space, clinging to the core of the
Warhammer Fantasy may, on the other hand, be conceived of as an alternate Earth: a world with an entirely different history, but significant similarities to our own.