It only talks about separating gas from the atmosphere. You then have to split up the molecules to do useful things with the atoms, and nitrogen in the air is triple bonded diatomic N2.
N2 gas takes 945 kilojoules per mole to split, while CO2 takes 393 kJ/mol. Since the thermodynamics aren't as favorable, the difference in concentration cost needs to be pretty good. Which it probably would be, (LN2 has been produced at scale for a century via cryogenic air separation and costs about a buck a liter) but green NH4 v green CH4 synthesis is not a slam dunk and it's not clear yet which one will be cheaper at the "replacing all transport oil consumption worldwide" megascale.
You don't even need to purify N₂ that much, as you can just add air to H₂ and feed that to the reactor, wasting some H₂ on O₂ but AFAIK it's quite cheap to enrich air to low-purity N₂ via pressure-swing adsorption, and it's just O₂ that's cheaper to get high concentration of via cryogenic distillation.
[Upon further reading, iron-based catalysts in Haber-Bosch synthesis are fairly sensitive to water as it promotes recrystallization of the high-surface-area needle geometry into more clumpy structures with less surface area and thus less catalytic activity; apparently it's thus preferable to cryogenically distill the oxygen out of the air to get by without a water-condenser-trap between the nitrogen feed and the catalytic reactor (ammonia condensing happens between reactor outlet and re-compressing to reactor inlet pressure).]
The bigger issue is that NH₃ (there is the ammonium cation NH₄⁺, but it's charged and thus needs an anion nearby to cancel the charge as coulomb repulsion would otherwise strongly limit the density of your (bulk) substance) is fairly toxic to inhalation when spilled, due to absorbing into water on the surfaces of your mucous membranes, eyes, and lungs.
It is technically also slightly toxic once in your bloodstream, but it's hard to experience that toxicity if you follow "GTFO once you smell" as most non-fish (mammals, sharks, amphibians, birds, reptiles, and terrestrial (i.e., non-aquatic) snails) have fairly capable metabolic excretion pathways due to protein "burning" (breaking down protein from old cells and food for energy) having ammonia as a waste product.
NH₃ is fairly toxic to fish because most assume they can just dump their own ammonia waste into the surrounding water and therefore rely on the surrounding water having concentrations far enough below what would be toxic inside the fish, as there needs to be some gradient to support the waste production/excretion rate.
I have a very naive assumption that the amount of energy needed to break apart molecules for fuel, is roughly the energy we get back when burning them.
N2 gas takes 945 kilojoules per mole to split, while CO2 takes 393 kJ/mol. Since the thermodynamics aren't as favorable, the difference in concentration cost needs to be pretty good. Which it probably would be, (LN2 has been produced at scale for a century via cryogenic air separation and costs about a buck a liter) but green NH4 v green CH4 synthesis is not a slam dunk and it's not clear yet which one will be cheaper at the "replacing all transport oil consumption worldwide" megascale.