It is shouting, you’re relying on a singular definition as though all-caps is the only manner of shouting in text. Disingenuous & rude.
Speaking of definitions.
a person who stealthily hunts or pursues an animal or another person.
He was shooting them at unawares from a space he deliberately darkened to avoid detection. He absolutely was stalking them using physical subterfuge. He did so over a prolonged period of time. That is all quite obviously stated. His pursuit was to photograph them at unawares in their home. Since he did not ask their permission or alert them to his doing it in any case there is no question at all he was stalking them.
It doesn’t matter if he lived across the street or in Bulgaria.