(a) It is a highly stylized example to illustrate game-theoretic concepts. In a sense I am asking the reader to imagine that THE GAME is about the runner getting to second or not holding all else about the game constant. That's not really baseball, but it is a baseball-like situation.

(b) The situation described is both vague (was the probability referenced by the color commentator for this runner? For this team? For this situation?) and specific (a specific runner/pitcher pair, there are zero outs not two).

(c) You are right about the goal of baseball. I had originally written it with the goal being scoring. But then it is a vastly more complex game.