Yeah, I am advancing the hypothesis that, in humans, the comprehension of indexicality relies on embodied pointing at its core [...] Whether all possible minds must rely on such a mechanism, I couldn't possibly guess. But I am persuaded humans do (a lot of) it with their bodies.

But wait; whether all possible minds must rely on such a mechanism is the entire question at hand! Humans implement this feature in some particular way? Fine; but this thread started by discussing what AIs and robots must do to implement the same feature. If implementation-specific details in humans don't tell us anything interesting about implementation constraints in other minds, especially artificial minds which we are in theory free to place anywhere in mind design space, then the entire topic is almost completely irrelevant to an AI discussion (except possible as an example of "well, here is one way you could do it").

In most European cultures, we use speaker-relative deictics. If I point to the southeast while facing south and say "there", I mean "generally to my front and left". But if I turn around and face north, I will point to the northwest and say "there" to mean the same thing, ie, "generally to my front and left."

Er, what? I thought I was a member of a European culture, but I don't think this is how I use the word "there". If I point to some direction while facing somewhere, and say "there", I mean... "in the direction I am pointing".

The only situation when I'd use "there" in the way you describe is if I were describing some scenario involving myself located somewhere other than my current location, such that absolute directions in the story/scenario would not be the same as absolute directions in my current location.

In a steep river valley in New Guinea, "down" could mean "toward the river" and "up" could mean "away from the river". And "here" could mean "at the river" while "there" could mean "not at the river".

If this is accurate, then why on earth would we map this word in this language to the English "there"? It clearly does not remotely resemble how we use the word "there", so this seems to be a case of poor translation rather than an example of cultural differences.

In a number of Native American languages, the pointing is always to a cardinal direction. [...] The cultural variability and place-specificity of language was not widely known to Western linguists until about ten years ago. For a long time, it was assumed that person-relative orientation was a biological constraint on meaning.

Yeah, actually, this research I was aware of. As I recall, the Native Americans in question had some difficulty understanding the Westerners' concepts of speaker-relative indexicals. But note: if we can have such different concepts of indexicality, despite sharing the same pointing digits and whatnot... it seems premature, at best, to suggest that said hardware plays such a key role in our concept formation, much less in the possibility of having such concepts at all.

How's this: "Embodied action in the world with a cultural twist on top" is the grounding point at the bottom of the symbol expansion for human meanings, linguistic and otherwise.

Ultimately, the interesting aspect of this entire discussion (imo, of course) is what these human-specific implementation details can tell us about other parts of mind design space. I remain skeptical that the answer is anything other than "not much". (Incidentally, if you know of papers/books that address this aspect specifically, I would be interested.)