Measuring humidity with Honeywell 5030/5031 sensors
The resistor is between the output and 0V of the supply. Minimum load implies it requires to be connected to a load to maintain a stable output, essentially it is there to prevent oscillation and false readings, as they are analog devices. 

Normally you might connect the output to an ADC of a microcontroller or data acquisition system and read the voltage output.
Often inputs into digital system have very high impedance, like around >1Mohm so the minimum load is there to ensure the device will draw the correct current to work.

You then need to take that votage reading and apply the conversion formula which is given in the datasheet. 
You might need to do a bit of algebra to the formula to get the actual humudity value. Also its a really good idea to have a temperature reading along with the humidity reading as there is a temperature factor involved to get a close to accurate reading.

I've had some experience with these particular sensors and they work quite nicely in normal temperature conditions. Just don't try and use them in very hot thermal chamber/oven type conditions or sub zero temperatures.
I hope this answers your question.

Edit: I will add that 65kohm is not a standard value, but 68kohm is, and I would say that would be close enough, by the time you have connected it to whatever you are connecting it to, it would below the 65kohm minimum load as lower resistance = more load ie. current.