Take that ammonium, burn it, have heat, power a steam engine, infinite energy?
Where does that energy come from? 1st law of thermodynamics?
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Professor Aldo Rossa started popularizing a lot of this in the 80s. https://patents.google.com/patent/US4107277A/en
Having something other than a fossil fuel source for the most common fertilizer in the world seems useful. Also, it's easier, cheaper and safer to ship ammonia around than Hydrogen since it's a low pressure liquid and more energy dense. People have been talking about using it as a shipping fuel for decades.
They have not given any numbers about the energy consumed by the pump, but at least in this experimental devices it is likely that the amount of ammonia that is produced is very small for the energy consumed by the pump, in comparison with other synthesis methods.
For now, the ammonia is produced as a solution in water with very low ammonia concentration. Perhaps this could be usable directly as a fertilizer for plants. For any other uses, concentrating the ammonia produced in this way would require a large amount of additional energy.
In the form presented now, this method of ammonia synthesis would be too inefficient, but the authors hope that the efficiency can be improved some orders of magnitude.