Confusion over the rate law
Rodrigo de Azevedo's answer can be stated with words by saying that the rate of the reaction is the rate of disappearance of $1$ mole $\ce{O2},$ and also the rate of disappearance of $2$ moles $\ce{NO}$. That is why the coefficient $2$ appears in the law written for $\ce{NO}:$
$$\frac{d}{dt}[\ce{NO}] = - 2k[\ce{NO}]^2[\ce{O2}]$$