What does the phrase "stone-gloved first baseman" mean?

Solution 1:

The first baseman's most important skill is catching balls batted and especially thrown to him in his glove. A "stone glove", which would make catching balls extraordinarily difficult, is a conventional metaphor for inability to catch balls and, by metonymy, for lack of other defensive skills.

Incidentally, Throneberry seems to have been a fairly average defensive first baseman; but he made a lot of defensive errors in his first year with the Mets.

Solution 2:

If a glove were made out of stone, it would not be very flexible, so it would be difficult to catch a ball in it. Combined with your finding of a reputation of "worst defensive player", the implication is that balls frequently fell out of his glove.

Solution 3:

Though @StoneyB's answer is functionally correct, I think it's important to note that Krauthammer was borrowing from a long tradition of describing someone who can't catch the ball (in the field sport sense) as having "hands of stone" (see, for example, here). In Krauthammer's usage, he's modifying it to accommodate the sport of baseball, wherein the fielding team is wearing gloves to facilitate (or not, in the case of Throneberry) catching the ball on defense.

What's fascinating about this usage is that it was completely overwhelmed in popular (English-speaking) culture by the description of Roberto Durán (the Panamanian boxer), and the movie made about him by the same name, and so any search for it requires some diligence at filtering out those usages.