What they call 'quantum teleportation' isn't teleportation in the Sci-Fi sense of some kind of matter transporter. Rather what they're doing is transferring information about the state of one system to another system. I.e. you have one atom in some state and you transfer that to another atom (of the same element).
The point of this is that you transfer the state without having performed a measurement (in the quantum mechanical sense), which could be useful, for instance, for transferring the state of a quantum computer.