That script seems to just select the next element of the mesh by advancing the element index, it doesn't take direction into consideration. A way to do what you want is to take the selected vertex and all the other vertices that are connected to it and project them all to the screen. With this you have a bunch of 2D…
There isn't anything like that that's built-in but it's certainly possible to do with a scripted add-on (it's like a plugin) that would add this new selection method.
I actually found this pretty useful in Maya as well, when trying to quickly edit on a per vertex level and you can't do it all at once. Yet to find a script for this in blender..bit out of my depth to do it in python.