"The supernatural" in this case seems to stand specifically for supernatural agency (personified invisible actors): presumably belief in an impersonal supernatural force or law (karma, say, or cosmic libido) would not be explicable in terms of hyperactive agency detection, or infantile theories about how the world fits together.
The video did mention a couple of other cases of the "supernatural" outside of invisible actors...the one that sticks out in my memory is the experience of
feeling someone looking at you who is behind you or outside your range of vision. I thought that was an interesting example, but a strange one, too, because reading the comments it seemed people were split--some have this experience often, others never have it. I have often felt this and looked up and saw someone there. (There's been speculation about mirror neuron hypersensitivity in bipolar and schizophrenic people. Anyway, highly speculative and for another thread...) But in each case, I'd doubt that "seeing" played any role in this perception, and that hearing or other senses play a much larger one. Since these are usually less conscious (smell, for instance, is something we rarely consciously perceive, in part due to olfactory fatigue), people tend to conceptualize or verbalize the sense of being watched in terms of "seeing" or "feeling" via a sixth sense. It's actually their regular old 5 senses that get the job done, but these work below the threshold of the conscious mind most of the time.
Something like "libido" I suppose you could explain chemically/socially/psychologically/etc, it would just be very very difficult to account for so many factors at once, and so people are basically forced use a metaphorical term that encompasses all of these broad categorical factors at once. That's why sexology is so difficult to research and such a messy, terminally interdisciplinary field.
Possibly interesting relative to this discussion is the way ANT reconfigures the agent/non-agent distinction, so that agency is redistributed among a great many kinds of entities acting on each other, if not purposefully then at least with some kind of teleonomic self- or reciprocal regulation. This is at least sufficiently close to pansychism for the question of the boundary with pansychism to arise. But it is still a fair distance from animism, precisely because Latour's actants are not personified - whatever agency is predicated of them, it isn't bound up with taking the intentional stance towards them, i.e. positing beliefs, intentions, symbolic representation of goals (although they may have "unconscious" "goals" in a teleonomic sense) etc.
Yeah, ANT is interesting to me for the reasons you mention up there (although I'm not a panpsychist)... I also think it meshes pretty well with information theory, bioinformatics, systems sciences, etc. It's almost like taking a world apart, taking each thing that goes into making that world (even a thing like a fantasy or a thought) and assigning it a random string of ones and zeros--so each thing is equally real and equally part of that world but the role that it plays is still indeterminate and can change according to any number of factors--then putting it all back together. Or at least, trying to do that. It's a nice way of attempting to sidestep the overemphasis on "the name" and language and anthrocentrism in most 20th century philosophy, anyway.
