As Leonidas mentioned, the original project wasn’t designed for a dynamic path.
You would need to change it or write a completely new script that would always check what’s the closest point that is in front of the camera. This can be done with a simple distance check from the camera/current point to all the other available points.
The other issue is that that project is using curves for the path generation which is calculated at the beginning and the curve is constructed taking into account of the points behind and ahead of the current point.
If this is going to be a dynamic path, I would consider changing the behaviour so that the camera is steered by the path so you can still get the smooth movement without using curves.
Honestly, it is probably easier for you to write a new script rather than using this as a base.