Why doesn't the expermintal molar solubility match the one calculated by the Ksp value?
The $\mathrm{p}K_\mathrm{sp}$ value of $15.69$ for $\ce{HgCl2}$ given by your reference must have an error. First of all, $\ce{HgCl2}$ is fairly soluble in water at $\pu{20 ^\circ C}$. Wikipedia lists it as $\pu{65.7 g L-1}$, yet lists solubility of $\ce{Hg2Cl2}$ as $\pu{3.25e-4 g L-1}$. Meantime, I found an University of Arkansas, Little Rock website, which has listed $K_\mathrm{sp}$ value of $\ce{Hg2Cl2}$ as $\pu{1.43e-18}$ ($\mathrm{p}K_\mathrm{sp} = 17.84$).

The molar mass of $\ce{Hg2Cl2}$ is $\pu{472.09 g mol-1}$. Thus, theoretically, the solubility ($s$) of $\ce{Hg2Cl2}$ can be calculated similar way you did:

$$s = \left({\frac{\pu{1.43e-18 mol3 L-3}}{4}}\right)^{\frac13}\times \pu{472.09 g mol-1} = \pu{3.35e-4 g L-1}$$

I think this is close enough. :-)