How can I determine what type of logic structure this circuit represents?
You can determine the functionality by analysing which transistors are controlled by which inputs.

Make a list of which are turned on or off when a given input is high and low.

Then make a list of which transistors need to be turned on in order for the output to be high or low.

Compare the two and you'll be able to build a Karnaugh map for the circuit.

From the Karnaugh map, you can get the SOP terms, and simplify them using boolean algebra. This will give you the answer which is indeed one of those three options.