You are correct that N2O is the "nitro" afterburner used in different systems.
But the reaction 2 N2O => 2 N2 + O2 is very exothermic, in fact it is explosive (but not in the burning sense, since its autodecomposition). However adding a small amount of ethanol makes N2O stable so that sudden shocks or compressions don't result in initiating autodecomposition or explosion.
To power an engine one doesn't necessarily need to burn, or a redox reaction to happen, the reaction just needs to be exothermic and N2O is very exothermic.