IOW, you can only say one computation implements another if there's a polynomial time reduction between the two that benefits from having the other as an oracle, which is not the case for waterfalls and chess.

That is a very concise and informative way of stating it.

The Turing Test, as well as human-run tests in general (like a quiz in school) can be subsumed into the concept of interactive proofs, where assumptions about the subject plus random probes of their knowledge suffice to prove what they are capable of, without knowing how they implement or represent it.

When considering whether a machine can pass the Turing Test, the relevant question is not if it's theoretically possible, but if you could do it while only using resources that increase polynomially in the length of the test (rather than e.g. a superexponential lookup table).

These are interesting points of view, which I tried to probe more deeply, or at least offer some counter views here. I think most people felt I was just bashing Watson, which wasn't my intention. Chapter 7 of the new book The Beginnings of Infinity by David Deutsch also spells out a good reason why hardware and software concerns beyond the guarantees made by an interactive proof Turing test might be necessary to really capture what we might want to mean by intelligence.