Smooth-pursuit eye movements require something to pursuit. Intentionally attempting to make such an eye movement in the absence of an appropriate moving visual target will
result in a saccade instead.
Your question concerns two types of basic eye movements, namely saccades and smooth-pursuit eye movements.
Saccades are rapid movements ...
There's a history of being amazed at similar ability that has led to some extra-scientific theories about it (see for example "psychic staring effect" on Wikipedia).
A better explanation is that gaze is very important to survival in the environment, and even more so for social species like humans. Even infants show sophisticated gaze detection ...
In theory you can use the geometry of your setup to transform your data to the orientation reffered in the paper you mentioned using Scheimpflug Principle and then use the methods provided in it.
Practically, you can only approximate the geometry of your setup. If you have some idea about angles in something like this
please let me know, I might be able to ...