What is the load resistor in the circled stage of the amplifier? If there is a load resistor, what is it's value (either in strict numerical value and/or in terms of the stage's small-signal model parameters (such as gM and r0))?
The load resistor is RC2 for the circled stage. In the schematic it is 4.7K ohms.
The emitter resistor RE2 is bypassed by the C1 capacitor to greatly increase the AC gain of the stage. The DC gain of that stage is ~(4700/1600).
The immediate load of that stage is RC2, which is 4.7 kΩ.
However, the input of the following stage also presents a load to AC components of the signal. That load therefore does not effect the bias point of the second stage, but does effect its overall gain of AC signals. At sufficiently high frequencies (we can't tell how high since the value of the various capacitors is not shown), the load on the second stage is R3 in parallel with R4, in parallel with the apparent impedance looking into the base of Q3.
From simple observation, we can see that R3 and R4 are "high" relative to the existing 4.7 kΩ DC load. At high enough frequencies, the impedance looking into the base of Q3 is RL reflected back to the base. This is roughly RL times the gain of the transistor. That again should be "large" relative to 4.7 kΩ.
Therefore, the conclusion is that stage 3 presents minimal loading to stage 2, and can be largely ignored, at least for a first pass analysis.