https://en.wikipedia.org/wiki/NOx
While natural gas is cleaner than coal in some obvious ways (i.e., no particulate solids), it has a specific problem with NOx, because of the super high temperatures inside internal-combustion gas turbines. The upside is higher thermodynamic efficiency (highest of any thermal source); the downside is, this.
EDIT: didn't see your edit until now. Heh it shouldn't be too hard to scrub out if it were really a problem. That seems like a better way to handle it than this weird exemption process that seems to be in place now.
Fuel NOx is only one of them, which you quite rightly point out is not dominant in methane combustion due to the rarity of nitrogen in the fuel.
The dominant source in methane combustion is thermal NOx, which forms due to the extreme temperature of the combustion, causing atmospheric nitrogen to decompose and react with atmospheric oxygen.
Source: https://www.epa.gov/sites/default/files/2020-09/documents/1....
The entire point of this dispute is that xAI could install scrubbers for these emissions, but chooses not too. The Ars Technica article discusses this at great length.