Next time you dress a deer notice that the lungs are much thicker up high than they are down low in the chest. The more lungs you cut the faster the heart has to pump blood to try and make up for the loss in blood pressure which causes the blood to leave the animals veins and arteries faster which deprives the brain of oxygen faster. It has nothing to do with drowning or the body cavity filling up with blood.

The deer will actually pass out up to a minute or so before its heart stops beating and it is actually is dead.

However, if the deer ran 200 yards I highly doubt that he actually got a double lung hit. I'd be willing to bet that the animal was only shot through one lung. A T.V. hunter would never make up something to cover his butt with millions of people would he.