I expect some people will be surprised by those words.It doesn't really matter.
In The natural way to say this is, "She has played different sports", the speaker/writer is presenting the statement as a fact.
In The natural way to say this would be, "She has played different sports", the speaker/writer is possibly tentatively distancing the statement from 100% certainty/factuality, or possibly presenting it hypothetically: If I were asked to say what a natural answer was, I would say ... . We cannot say for certain. I doubt if the speaker/writer could say for certain. It doesn't really matter.
So the use of "would" in "the natural way to say this would be..." indicates a hypthetical, is it right, jutfrank? It's not tentative.The only part I disagree with here is that would in such an utterance could be used for tentative distancing. If the speaker wanted to distance himself from the statement, he's far more likely to use a qualifier like I think, or use would with a prefacing 'opinion' verb (I'd say, for example). It seems pretty clear to me that the speaker here intends to speak authoritatively.