To be honest, I don't know why it's called artificial photosynthesis versus photovoltaics - perhaps it is because this research looks to the actual chemical systems involved in photosynthesis as models for man-made systems (as opposed to trying to develop light-converting systems ab initio). In any case, "artificial photosynthesis" is commonly used to refer to research both on hydrolysis via solar energy and carbon fixation into organic compounds, both of which are fundamental to photosynthesis as a whole.

I was wrong about the chlorine production, actually - it only occurs at high concentrations of salt. Otherwise (or with different solutes), you can produce oxygen. Still, I believe that this reaction is not efficient enough to be feasible as an energy source. Overall, you do want the hydrogen, but you also need an oxidant to, for example, run a fuel cell. I think there are hydrogen-chlorine fuel cells, but I imagine it would be easier and more practical to run a hydrogen-oxygen cell instead to avoid using chlorine gas/producing HCl. In any case, it boils down to developing catalysts to improve the rate and efficiency of this electrolysis (by lowering overpotentials).

I agree with you that your paragraph makes a lot more sense than the parent article. It's annoying how these press releases make things seem much more revolutionary than they really are.