The Earth's atmosphere is about 80% nitrogen and a little less than 20% oxygen, with some carbon dioxide, argon, variable amounts of water vapor, and some pollution.
My guess is parent comment misspoke and meant pure nitrogen -- which does indeed help with tire pressure. The ideal gas law still applies, so there will be seasonal changes in pressure, but there will be much less exfiltration (via 'permeation', specifically) of gas through the material (N2 has a larger 'kinetic diameter' than O2; O2 will permeate 3-4x faster through rubber than N2).
So if regular air is 80% nitrogen already, won't the tires move towards 100% nitrogen with each top off since the tires will be retaining the nitrogen more than the oxygen? Sounds like a marketing trick unless they're filling newly mounted tires with 100% nitrogen.
That's a pretty clever thought in general, but yours is only a first approximation.
First, permeation decreases with pressure, at different rates for the two gases. If you consider only this fact you will find that the partial pressures of O2 and N2 asymptotically approach homeostasis, rather than simply all the O2 leaving and all the N2 remaining.
Second, permeability changes with temperature, so the ratio of O2 and N2 exfiltration rate changes seasonally, as each gas has a different permeability-vs-temperature curve. Third, the ideal gas law causes pressure changes seasonally which will also decrease exfiltration in winter, and once again, each gas will have its own permeability-vs-pressure curve, so these become very confounding factors.
All in all, the reality of the situation is that filling up your tires with atmospheric air will probably settle on partial pressure ratios of, say, 85/15 rather than 100/0. The deflation that you get comes from only about 5% of the O2 leaving the tire; and of course you get another big deflation when the weather first turns cold.
I don't know the exact numbers because I've frankly never thought to look into this before. So like I said, it was a clever thought! But it needed to be taken a few steps further.
Maybe just nitrogen? Costco inflates tyres with nitrogen. The pair of tyres on my vehicle inflated with nitrogen don’t seem to lose pressure, the other two need topping up occasionally.
That at least helps with some of the logic. However, doesn't directly answer what "nitro oxygen" is. Guessing some sort of slang. It's definitely not a scientific phrase. Nitrogen oxide or something maybe too much for grease monkies so they call it nitro oxygen??? just guessing.
What's "nitro oxygen", then?