If he hadn't run, Beatrice would still have won, but it would still have cost him the $.20 of unhappiness at Beatrice winning, but at least he would have saved himself the C of running.
Alex ended up with a payoff of -C, actually more than that, C minus the distance between him and Beatrice, so that's another $1, $.05, $.10 or even $.20 whatever it is, and he would have done better to have not run.