Meaning of Flammability Limits and reaction in Air of Ammonia
Chemical reaction would proceed in an air/ammonia mix, even outside the concentration range at which the reaction is self-sustaining, particularly if there were a catalyst to help. It is just that at the specified concentration range, when it reaches $651^{\circ}\mathrm{C}$ at one point in the mixture, the reaction proceeds fast enough to heat the rest of the mixture to that ignition temperature.

This is similar to an Otto cycle spark-ignition engine: with the correct mixture, the flame front propagates from the spark plug throughout the cylinder.

In the Ostwald process, a $1:10$ ration of $\ce{NH3}$ and air can sustain the reaction at the surface of a catalyst.

In a similar fashion, hot copper can catalyze the oxidation of acetone, methanol or ethanol, providing a surface where the reactants can combine fast enough to keep the surface hot.