It could contain an artifact physically identical to one and which we could call one if we weren't being precise, but it would have to have come from some origin besides humans intending to build a chess set.

Do you seriously mean to imply that something identical to chess set is not a chess set? The words "chess set" as I used them above are meant only to connect to a physical object, not intentions.

Thus would be perfectly reasonable for the two to speculate (and be right or wrong) about what (if any) use it was meant for by its actual builders (if any).

In practical terms I agree completely. My argument with Peter wasn't actually about chess though, so it doesn't make a ton of sense when you focus on particulars of the analogy, especially an analogy so flawed as this one.

Do you think we disagree on any issue of substance? If so, where?