It may still be the same aspect. My recollection is that the levitation is due to the flux quantization that occurs in ringed superconductors. With a superconducting ring, the amount of magnetic flux through the ring is quantized and can only have discrete values. In addition, the Meissner effect allows for the fact that if we induce a magnetic flux through the ring and then make the ring superconducting that the ring will maintain currents to keep the magnetic flux going even when we remove the original source. So the Meissner effect and flux quantization allows us to induce a superconductor to produce and maintain a magnetic field that can allow for levitation. My guess is that this "locking in" of the position of the superconductor may be something similar to the flux quantization that allows the superconductor to maintain currents to maintain its state. It's important to note that with the magnetic track and other situations, there is an axial symmetry that was maintained. This allows the superconductor to traverse the track while remaining, for all intents and purposes, in the same state.
Probably of more interest in terms of progress is that we now have sufficient high temperature superconductors that he can use simple liquid nitrogen to achieve superconducting and be able to grasp and manipulate the metal for a period of time without it falling out of the superconducting state.
It shouldn't need to. The physics of the problem states that the quantum states of the superconducting current would react in response to how he positioned the superconductor with respect to the magnetic field. What I find interesting is that normally when we talk about levitating a superconductor, the textbook example requires us to start from a non-superconducting state with an applied magnetic field and then cooling the material down to superconducting to lock in the magnetic flux. Instead, he has already cooled the material down to superconducting and is continually readjusting the locked states. But, as I said above, I would imagine that the physics remains the same.