I don't think the analogy holds. River based directions can be mapped to NESW. It does't hold that the concept of "hey I ran out of stuff" would not exist in their minds. It is impossible that they didn't understand this concept.
Well, the may have understood the concept of "running out of stuff" and yet not realize it naturally belongs with numbers (of which they would have known other examples like one and two). I can imagine ancient folks putting the notion of "running out of stuff" with ideas such as "hungry", "empty", "dead" etc. Formation of the more abstract concept of zero-the-number is certainly a few cognitive experiences further down a line.
There are cultures where the basic directions are north, east, south, west, which they use pervasively in preference to forward/back/left/right. People from such a culture are very good at keeping track of their absolute orientation and are uncomfortable with body-relative directions.
"Hey I ran out of arrows" is a different construct than "there is such a thing as a number that is independent of particulars like arrows and zero is one of those numbers"