I would probably say "The last leg of the 600 meter race" as well. There may be other words that could be used that were activity specific. In some sports, a round is called a "heat" so it would be "the last heat." Depending on the race you could maybe say the "last lap" of the race if they're going around a track multiple times or "the final stretch" of the race if it's the end section. If it's a game, you would probably say "the last round of the game" instead.

I would translate it to: "The last leg of the 600 meter race" Maybe someone could come up with a better translation