I thought the song was perfect! To me it's about coming together after these weeks of competitions. We are all people after all. The "imagine there's no countries" line to me was about breaking down our divisions and what separates us and realizing that although we may compete against one another and in the bigger since, fight each other in wars, we are all very similar. "Imagine no possessions, I wonder if you can. No need for greed or hunger. A brotherhood of man." We place so much importance on things like winning medals and being the best when in the big scheme of things that's not what the games and life in general are about.
It's seriously one of the best songs ever written in my opinion. So simple but so complex at the same time. I think it's perfect for the end of the games as if to say these games were fun competing against each other but now it's time to put our differences aside and celebrate our similarities. I wish they would have used it when they were extinguishing the flame. The fact that it was such a contrast to the games made it just right.