As well as the technology to drop about seven letters from everybody's names and start going by 'Jon' or 'Robb.'
Even the disparate regions of both worlds match up. The Shire is in the North, where the children of the forest (Hobbits?) dwell alongside face-having Weirwood trees (maybe the Ents finally went full tree). The "men of the west" remain in Westeros, Gondor is Dorne, while Rohan is in Essos, its riders having journeyed eastward and intermingled with the warlike Rhun to become the Dothraki. As for Mordor, it's right about where Valyria was until "the Doom" -- a mysterious, allegedly volcanic cataclysm which proponents of this theory insist was Mount Doom erupting one last time, probably launching smelted Gollum bits clear out into space.
Here it is erupting in the opening credits.
As further proof, some fans even spotted Gandalf's sword, Glamdring, forged into the Iron Throne.