[RedDevil]

Laughing gas (N2O) is an oxidizer, they erroneously confuse it with oxygen (O2).
Of course there will be less free oxygen if they really manage to produce a reasonable amount of laughing gas, but the total amount of oxidizing molecules (either oxygen or laughing gas) would indeed be higher.

But 12 Watt is not enough to produce a reasonable amount of laughing gas, never mind whether it could have a benefit or not, never mind what method you'd use to make it.
They probably use static discharges. There will be ozone, and nitrogenmonoxide, and whatever, all in very small quantities.

If it affects the fuel economy at all it is probably due to heating, thus expanding, the intake air... an eWAI so to say.
But even then 12 Watt is way short of what you'd need. It would heat the intake air of even a small car engine by less than one degree.