Zn²⁺ has a radius of 74 pm and Mg²⁺ of 72 pm.

Step 1. The numbers. $\text{Zn}^{2+}$: $\dfrac{2}{0.5476} = 3.65$. $\text{Mg}^{2+}$: $\dfrac{2}{0.5184} = 3.86$.

Step 2. The shells. $\text{Mg}^{2+}$ has the neon shell, $2s^2 2p^6$. $\text{Zn}^{2+}$ has an $18$-electron outer shell, $3s^2 3p^6 3d^{10}$.

Step 3. Why. The $3d$ electrons shield the nuclear charge poorly. So the chloride ion feels more of the zinc nucleus than $\dfrac{z}{r^2}$ suggests. It is polarised more, and zinc chloride is more covalent, with a much lower melting point.