How is laughing gas produced in the Nef reaction?
The Nef reaction does not produce nitrous oxide directly. It produces nitroxyl as a reactive intermediate, which rapidly decomposes via a bimolecular reaction to nitrous oxide and water$^{[1]}$. You are correct that the base removes the alpha hydrogen; the nitro group is more than capable of accepting this negative charge. The crux of the Nef reaction is this:



The mechanism for the formation of nitrous oxide is as follows:





$[1]$ Wikipedia: Nitroxyl, Reactions