I think at this point you either need to lay out clear criteria (not examples, examples are easier than detailed standards) as to what constitutes horror and what doesn't. At the very least, there's no point in just saying "this is horror" or "this isn't horror" absent any further explanation, though.
I researched genres/subgenres for a website project and genres can be as subjective as films themselves, Many of the sources I used in research were literary basics/tutoring sources, but for certain all parent genres have subgenres and even subsets.
For example the parent genre Sci-Fi contains the Artificial intelligence subgenre. And drilling further down that subgenre contains the Synthetic Biology subset.
The same for the parent genre Horror. I've seen Thriller/Psychological listed as a subgenre of Horror. I've also seen Home Invasion listed as a subgenre of Horror. To make it more confusing, I've seen parent genres listed as a subgenre for another parent genre, for example - Adventure>Comedy, Sci-Fi>Horror, Horror>Thriller.
The parent genre Thriller also has subgenres:
Disaster
Psychological
Crime
Techno
Some films have a hierarchical set of genres/subgenres.
Primary genre/subgenre
Secondary genre/subgenre
Tertiary genre/subgenre
It's a judgment call what film's primary and secondary genres are.
For example, Alien 79
Primary genre/subgenre - Sci-FI
Secondary genre/subgenre - Horror
Or one could argue to flip which is the primary for Alien.
Another example, Thor Ragnarok (TR)
Primary genre/subgenre - Action/Adventure genre
Secondary genre/subgenre - Comedy genre
Tertiary genre/subgenre - Super Human Sci-Fi subgenre
Again, one could argue which one is the dominant genre/subgenre for TR, but one thing for certain, all three genre/subgenres are contained in that film.
And in the case of the film currently discussed, Manhunter
Primary genre/subgenre - Thriller genre
Secondary genre/subgenre - Horror genre
Tertiary genre/subgenre - Thriller Crime and/or Psychological subgenre
Again, one could argue which is the primary genre/subgenre.