"John, that wouldn't work. Follow the circuit if you move the LH switch to the other position ...."
I think you have to visualise the internal switch contacts from his sketch in order to see how it works -- similar to those in yours.
Obviously, the question was waaaaaay easy.
Regarding your (neat) sketch of two-way hall switching, what alterations of the circuit would be needed in order to switch the lamp on/off from THREE separate locations?