What exactly does the "per mole" unit of heat of atomization mean?
According to Wikipedia,


  Standard enthalpy of atomization is the enthalpy change when $1$ mole of gaseous atoms is formed from its element in its defined physical state under standard conditions $(\pu{298.15K}, \pu{1 bar})$.


$\Delta H_{\text{at}}^{\circ}$ focuses on the production of $1$ mole of atoms from the element. Hence it's defined for the reaction: 

$\ce{\dfrac{1}{8}S8 -&gt;S}$ 

but not for the reaction: 

$\ce{S8 -&gt; 8S}$

So whenever you see the term "per mole", it is, by definition, implicitly referring to the product and not to the reactant.