Which zero load condition should I use when trying to find Ri?
Zero load, defined in our class, is when \$I_{out}=0 \space or \space V_{out}=0\$. I was trying to solve this current mirror circuit, and I am confused why \$I_{out} = 0, \space not \space V_{out}=0\$.
Zero load, defined in our class, is when Iout=0 or Vout=0
You may be misinterpreting it. Zero load with a resistive load is when Vout=0. But that's the only case when Vout=0 means no load: it's 0V across the load resistance, and thus implies Iout=0.
In other words:
$$ \Im(Z_L)=0 \implies \biggl( V(Z_L)=0 \implies I(Z_L)=0 \biggr) $$
The reverse implication is does not generally hold, i.e. Vout=0 doesn't imply Iout=0.
Zero load does generally mean only Iout=0, and doesn't imply anything about voltage unless a specific kind of a load is discussed.
The circuit you are showing is not a current mirror, but a common gate stage with a current source load. The current source load is a current mirror, but the input of the circuit is the source of Q1 and the output is the drain of Q1. Q1 is a common gate amplifier.
The input impedance of a common gate amplifier depends on the load impedance. You can see this by analyzing the circuit with a general load, Z, and setting Z=0 or Z=infinity to evaluate both I=0 and V=0 output conditions. This is probably done in several textbooks, Design of Analog CMOS ICs by Razavi has it for sure.
