Apples and oranges.

Hardball (i.e. baseball) is a different (but very similar) game than softball. To play hardball in the metaphorical sense probably gets its name from the fact that it hurts a lot more to get by a baseball and that a baseball can be thrown harder and faster than a softball.

I take "to quit while he's still got his fastball" to mean that he is going to quit while he's at the top of his game, or in his prime. For most major league baseball pitchers (and fast-pitch softball pitchers), the ability to throw a really fast fastball declines with age. (There have been some pitchers with long careers, however, like Nolan Ryan, who played 27 years and threw very fast fastballs into his forties).