What part is considered late game?

I was always under the impression that early game was prior to 20:00, middle game is 20 to 35, and late game is after 40 minutes.

Is that completely wrong?

Riot seems to think so, as they're claiming Xin is forced to go for "Late" game strength when he buys Devourer, which he and any other champion that it's too strong on can get Sated easily before the 20 minute mark.

Edit Thanks for the feedback, but it seems you actually agree that the point where champions get Sated and one item to proc with it is nowhere near late game.