The meaning of ad-hominem is easy enough to lookup. Both your examples are ad-hom, one is less relevant than the other. In neither case are you addressing his argument rather attacking the speaker's motives or character. "How old are you?" is both snarky and ad-hom, moreover the questioner knew he was being snarky.
> how old are you?
The great thing about this rhetorical device is that it is both a fallacious and non-fallacious ad hominem. Asking the persons age is a legitimate question given the question of how important NYT is to public life. It's also a legitimate dig. "Ah. I see what you've done here."
I was under the impression that ad hominem is about dragging irrelevant personal qualities into the debate.
For example: the topic is water quality. Joe Bloggs is troubled by the effects of pollutants in tap water.
Not an ad-hom: "He owns a company which manufactures tap water filters".
Ad-hom: "He's an atheist".