The problems are a little more subtle than that, I think. The study was of middle aged runners and non-runners over a 20 year period. It didn't include any elderly, apparently. So the anti-correlation here is between death in middle age (what most people would term "dying early") and running. There is no correlation shown for the lede of the article, which talks about living a "long life". There's evidence that runners don't die young as often, not that they live longer.
As far as causation goes, I don't have too much of a problem with that. The clear hypothesis would be that runners have stronger hearts more capable of dealing successfully with degenerative conditions like heart disease, and therefore they're less likely to die of a very common killer of the middle aged. The hypothesis isn't proven by the data at hand, but is at least very strongly suggested.
As far as causation goes, I don't have too much of a problem with that. The clear hypothesis would be that runners have stronger hearts more capable of dealing successfully with degenerative conditions like heart disease, and therefore they're less likely to die of a very common killer of the middle aged. The hypothesis isn't proven by the data at hand, but is at least very strongly suggested.