Officially, the Korean War has never ended. There is an armistice. So the phrase means that if the Chinese broke the ceasefire, if the Chinese attack, Eisenhower had the option to use atomic weapons. "Should he decide to do so" (should he choose to use atomic weapons), "if the Chinese broke the ceasefire" (if the Chinese attacked).
And yet it was the USA that broke the armistice, bringing in nuclear
weapons despite their being banned. It was the USA that continued
and continues to this day, a reign of terrorist actions against the people