Let's take the ability to match the best humans at various tasks. If we put doing long multiplication better than the best human at "1", and passing the Turing Test at "10", where is a Go playing engine? I'd say less than "2", but still higher than chess.
Much higher (but still short of general intelligence, obviously) would be beating the best humans at language translation, proving math theorems, or answering factual questions phrased in natural language. Then, if and when computers can write novels which you'd prefer to read over the best human author, now we're talking.
So I think, we don't need to worry about our humanity here yet, and we're not remotely close. Over less than a century we've gone from outperforming humans in arithmetic to outperforming us in things that are a little less like arithmetic but still discrete games modeled by trees and precise searches.