i haven't looked at the file but basically what the pointSOP is doing is computing a new normal direction. for you example for the $NX component based on the current value of $TX minus the second input's value for $TX, that's where the $TX2 comes in. So when you see $TX it means the ‘x’ component for all the points in the current geometry.
Try this as well to help.
Put down two grids with the same default settings. Append a facetSOP and toggle on the compute normals option for both. For one of the chains append a transformSOP and move the the grid up and over 1.5 units in x
Now append a pointSOP off the other chain. input the transformSOP into the second input of that pointSOP. Try the following:
T(urn on the display of normals first)
in the normal field where it says $NX put $TX2-$TX
You will see the normals of the 0,0,0 grid aim at the transformed grid.
I'm sure there are better ways to see this stuff, and more people here have different examples but that's mine without houdini infront of me

-k