How can I measure a sensor's load resistance which is adjusted by a potentiometer?
The MQ series sensors have two circuits within the sensor.

The first is the heater circuit which is connected to a voltage source and this heats up the active element.

The second is a chemical sensor which has a variable resistance according to the concentration of the target gas. The resistance of the sensor varies wildly between different sensors.

The sensor is connected in series with the load resistance to produce a voltage, due to the variation in the sensor resistance this is the pot you have on the board. Adjusting the pot adjusts the output voltage. Generally the rest of the circuitry is a voltage comparator set to raise or lower an output when the voltage from the sensor-Rl section reaches a set level.

To measure Rl measure the resistance over the pot. It is impossible to tell for sure from your description but I suspect the LED comes on when the output voltage from the sensor-Rl combination lies within a certain range. Measuring the voltage at the junction between RL and the sensor while adjusting the pot will give you some insight into what is happening with this particular circuit.