This thread from July 2009 offers a couple thoughts.
* A combination of gathering greens and tucked pins. I could see how those factors could favor someone with a more "plodding" mindset, potentially.
* Lots of wind, which might favor a slower swing speed player who generates less spin and a lower ballflight, especially if that player is one of the great links players in the history of the game.
* Firmness. I think that one's almost a given - with the ball running out, Watson wasn't at a terrible disadvantage in terms of distance. And with greens not allowing for drop-and-stop approaches, a well-carved 8 iron could be just as accurate an approach club as a high, soft wedge. Of course, a 9 iron might work better sometimes...
Just as an aside - like Jeff, I think about what might have been. I'm not really a Watson fan, but I was that week just like everybody else. In hindsight though, what DID HAPPEN is still pretty amazing. It's one of the great tournaments I've ever watched - I remember where I was and what was happening in my life at the time, and yet, I don't remember a single shot that the winner hit. That Open belongs to Tom Watson, even if the Claret Jug didn't go home with him, and it adds a lot more to his legacy as a great player than it takes away.