"World's first 3D people mover" might be a more appropriate --- and enticing --- title, because "rope-free" can also refer to hydraulic elevators (which have been around for over a century.)
As far as I can see, the design only allows 2D movement. If you wanted the lift to move toward or away from the camera, you would need either some kind of 2nd attachment point on a different side.
Or a vertical segment could have a curve too. Imagine rotating by 45 degrees as you go up ten floors -- suddenly now you're in a completely different plane.
We could also check whether "The Willy Wonka elevator" arouses more curiosity: It's a feature of the Charlie and the Chocolate Factory book (and in the movie from Tim Burton).
3D Railway Pod? Seems like it follow tracks and switch lines like a train only it can also go up and down. It's a step close to the Great Glass Elevator.
