I'm amazed that buildings tolerate this kind of stress, or maybe I underestimate how accurately they can apply equal pressure to rotate the building safely.
Assuming it has a properly-designed & constructed foundation (which, if the building tolerates just being there at all, especially for decades, it probably does; but this is something that would be checked anyway), it's just a matter of adequately supporting that and taking everything slow. After all, the foundation supports the entire building, so moving the foundation will move the building. The stresses involved here (this Twitter thread says it was moved 15 inches per hour) are practically nil; it also says the people inside didn't even notice it happening.
