This Brodie Sinclair guy might be an lolcow himself...
The fact that he seems to be palpably insane is very relevant to a potential defamation suit. The standard for defamation of a public figure (which David Geithner almost certainly isn't but I'll get to that in a bit) is actual malice, which doesn't mean the standard English definition of ill intent but instead, specifically, knowledge that a defamatory statement is false or reckless disregard as to its truth or falsity.
Reckless disregard is generally negated if the defendant can show they reasonably believed the false statements. That is, even though the statements later proved to be false, the defendant engaged in some degree of due diligence and didn't just rush to press with crazy garbage. The fact that this "confidential source" appears absolutely batshit, though, would tend to mean that Gawker could not have reasonably relied upon such a person as a source of accurate information, and was required to do more to verify these facts.
Now, this isn't entirely relevant to pure issues of liability itself, because David Geithner is almost certainly not a public figure. Just being related to someone famous doesn't make you a public figure, and he did nothing in this story even to be considered a limited public figure for some purposes.
Someone who is not a public figure can successfully claim damages for defamation simply by proving the statements false and that they were made merely negligently. The standard is less strict, and is merely that a reasonable person would not have published the allegations in question.
I think the outcry over this reprehensible, scurrilous article is pretty indicative that this is the kind of outrageous conduct that is viewed as unacceptable in a civilized society, and is not likely to be considered reasonable.
However, the fact that the motivation for the piece went beyond mere negligence into conduct that would even defeat a motion to dismiss filed by a public figure would provide a good argument for punitive damages in the case of a successful lawsuit, i.e. the defendant should not only have to pay for damages caused, but additional damages to punish them and send a message that this kind of behavior will not be tolerated.
In short, even in a legal environment fairly hostile to defamation claims, that is, the United States in general and New York state law specifically, this is the kind of case a defamation plaintiff's lawyer dreams of.
Assuming there were substantial falsehoods in the story, that is.
