I agree that baseball is a wonderful game. And its one that I enjoy watching with others. And just about anyone can understand it. When my wife watches football its like the dog watching tv. She sees movement but doesn't really understand what it means. But she can watch and enjoy a baseball game with no problem.
I stopped watching baseball when they went on strike and I stopped watching hockey when they did it too.
Although I agree that there is a good deal of strategy in baseball, I wouldn't say it was unique in that. It is interesting that it would be called a "thinking man's" game, which I agree it is but not sure how much so related to other sports. Wouldn't football be the ultimate strategic sports game?