Of course it is energy net negative. There is an energy cost to reducing nitrogen to ammonia. Enzymes aren't magic and nothing changes the energy cost equation of the products vs the reagants.
The reason we need these complicated processes is the massive activation energy of the reaction, making it extremely slow uncatalyzed.
These are professional chemists, publishing in a serious journal. Did you really think they didn't take into account the basic energy balance of their equation?
The reason the Haber process is so costly is because it uses very high pressures and temperatures to overcome the activation energy, even with the best catalysts we have. Not because creating ammonia from nitrogen and hydrogen needs energy. It's in effect wasted energy.
Enzymes can't change the cost equation, but luckily it's in our favor. If they can reduce the activation energy without wasting a ton of energy, it can be a net energy producer.
0: https://en.wikipedia.org/wiki/Ammonia 1: https://en.wikipedia.org/wiki/Haber_process
However, I was refuting the GP's wrong assertion that the energy cost equation of this reaction shows that it cannot be a net energy producer.
It makes sense to optimize this step, because the energy equation shows the energy is just wasted as heat, as it's not contained in the compound itself.
The article is not purporting to have conceived of a new energy source, only to have found a way to recuperate some of the cost of making ammonia, by extracting some energy from a step that ought to be a net energy producer.