Is this "teleportation" supposed to be the same as quantum tunneling or something else?
Quantum tunneling is completely different. Tunneling is basically where electrons (for example) are "leaking" out of the confined space they are supposed to be travelling through. A more technical explanation is where "a wavefunction can propagate through a potential barrier." (wikipedia)
Teleportation is where the state of one quantum particle can be instantaneously imparted onto another quantum particle, essentially making the second particle indistinguishable from the original. This is quite similar in my mind to quantum entanglement in which 2 particles are somehow "connected" in a way that if properties of one particle change then the "entangled" particle also changes to match without the need of any human action in order to force the issue. I believe in most quantum computer setups, they are leveraging the "entangled" particles whereas AMD seems to be pursuing the idea of using teleportation instead. This saves the hassle of keeping particles entangled (tricky as entanglement is hard to maintain) and instead just forcing a teleportation each time it is needed.