They do a quarter quell every 25 years, but not just champs vs champs. IIRC, one was 4 tributes from each district, and the other was people voting on the participants instead of random. The champs playing is implied was a farce to kill of Katniss Everdeen :) as she became a rallying point for the revolution when she defied the capital (ie faking suicide pact with the berries in the first movie/book)
They did not get two from each district. There are a total of 75 champs to choose from, not all are still alive, but there are still enough to choose from, ex. district 12 had 3 living champs...2 went. where districts 1 and 2, had many more, but only 2 went from each.