For anyone interested in the actual paper, it's H. Song, et al., Nature 462 p. 1039-1043
As a (biased) researcher in the field, my opinion of this is that it is no more than an attention grab and will do little to advance science (this is pretty typical of Nature papers, though):
1. The contacts are still very large compared to the channel (what they call the "transistor"). Without advances in scaling down contacts, you won't see a meaningful decrease in transistor density from this technology. What's more, they don't include an actual picture of the device, so there's no way to tell how big the contacts actually are.
2. Like most researchers, they "cheat" and use a very large (probably macroscopic) back gate to modulate current. The idea of a field effect transistor is that you apply a voltage perpendicular to the direction of current, which causes charges to move along the electric field and either hinder or help transistor current by creating (or eliminating) a potential well in the transistor. In real devices, you have billions of these transistors on a single wafer and so at some point you have to actually place a local gate, which usually has a huge negative effect on transistor operation.
3. They don't appear to have any good way of controlling how many of their transistors work (they rely on chance to get these molecules to bridge the gap between electrodes)
While certainly thought-provoking, as an engineer I am not particularly impressed until I see them using scalable methods.
Scientists Create First Functional Molecular Transistor