First things first. The quantum teleportation protocol requires classical bits to be sent from Alice to Bob. Without these bits, Bob cannot apply the proper corrections to actually obtain the desired "target" state $|\psi\rangle$, this is apparent by understanding what's going on in the teleportation protocol.
Additionally, the requirement of a classical channel in the teleportation protocol eliminates the notion that quantum teleportation could be used to send information faster than the speed of light, which should be impossible by other physical laws, see the no-communication theorem.
From quickly glancing at the article and this "simplified" teleportation protocol, it seems that the author is not proposing that you can do teleportation without sending any classical bits (at least I hope that is not their claim), but rather, they seem to be analyzing the quality or fidelity of the teleportation protocol in the case where you don't send the classical bits. This is all fine, but it should be stressed that this protocol will only work a small proportion of the time.