Probably ammonia will be a better transport medium than hydrogen, but you need hydrogen to make ammonia.
We need ammonia for fertilizer, and right now we get the hydrogen for that from methane, which can't be the plan long-term. At the moment switching to hydrolysis would double to quadruple the cost of the hydrogen, but eventually falling electricity and rising natural gas prices should invert that. The Haber-Bosch process itself doesn't require petrochemicals, it's just the cheapest way to run it in the current market.
The intent of the method presented is to make electrolysis energetically cheaper. It might end up financially cheaper, depending on what the apparatus costs, which will of course start out high and come down if used much.
Apparently there are practical catalytic processes to go directly from N2 and H2O to NH3 and O2. Everything will compete, and a few processes will win. Tolerance of impurities in the water has often been a problem. Where you have to distill the water first, that increases cost.
I could imagine it as a viable storage technology, e.g. if you want to install a solar farm in a remote location you could have it produce hydrogen from the air and sell that.