When considering a variable, decreasing load \$ R_L \$,
$$ R_L I_L = R_L (I_S - I_Z) = V_Z $$
can be constant as far as the Zener diode balances the reduction of \$ R_L \$ by decreasing \$ I_Z \$, so: the Zener diode regulates the voltage. When \$ I_Z = 0 \$, the diode is useless and the resistances \$ R_S, R_L \$ determine the voltage across it, so they "regulate" this voltage. It seems that the Zener diode needs an external circuit (like the one composed by \$V_S, R_S, R_L \$) which can put it in reverse bias, and it can become a regulator only after this condition is reached. Otherwise, it is useless and its voltage is determined by the remaining part of the circuit.
Then, who is the actual regulator in this circuit? The diode or the resistances?