Chemistry - Why does NOCl dissociate as +NO and Cl-?

Firstly, the correct comparison to make to determine which is more likely of $\ce{NO+}+\ce{Cl-}$ and $\ce{NO-}+\ce{Cl+}$ is the ionization potential vs. the electron affinity of the the two species. The electronegativities are correlated with these other metrics, but it is important to emphasize that those are really the important things.

Relatedly, nitrosonium $\ce{NO+}$ is stabilized by resonance and so this is a considerably stabilized cation (i.e. IP not too high). On the other hand, the IP of $\ce{Cl}$ is huge while the EA is small; it would much rather get an electron than lose one. The hyponitrite anion $\ce{NO-}$ actually usually dimerizes for reasons outside the bounds of the question. So $\ce{NO+}+\ce{Cl-}$ is way lower in energy.

In general, a red-flag should go up when you see halogens with positive charges. They do happen, but very rarely, especially at the level of chemistry in an intro organic course.