That was past; then came the deal to an armistice to end the Vietnam War (though then after the armistice NVA and VC continued the war and South Vietnam collapsed). The point of that prize was not that there had been war, it was that the parties had signed to end hostilities.

In 2009, the peace prize really was quite strange in my opinion: Obama had achieved rather little except winning an election campaign (becoming the U.S. president the same year) on promises that undoubtedly sounded good to the Committee (but which later on were not kept very well or quickly).