From the same account:
"...But until some satisfactory witness can be found of the love of that age for knowledge and: discussion, we had better let the matter drop, and give the reason why we have unearthed this tale, and then we shall be able to get on."
Seems clear to me that Plato understands this as a myth.
That isn’t the point. The point is that one of Plato’s characters refers to antediluvians as “nurselings of Cronos” in such a natural way without bothering to explain the reference, i.e. he took for granted that the whole world of his age understood the reference.