Here's the context of my quotation. NY Magazine writer Choire Sicha wrote "For obvious reasons (Caucasity), most of these reporters are on the joyless, scold-y White Twitter...."
In the comments, Lucien said: "'Caucasity'? Is that like 'whiteness'?" And Clyde said: "'Caucasity'?! What bilge!"
To answer Lucien's question, "Caucasity" clearly means "whiteness." Why use an odd word when there's a more common word? I'd say it's just for humorous effect. It actually takes race less seriously. "Caucasian" used to have a somewhat elevated quality, when race was palmed off as a biological science. To seize upon the big word and to further enlarge it with an ending is a standard humor move. It's actually quite old fashioned.
But I just want to question the choice of ending — "-sity," rather than "-city." I've googled Caucasity" and got thrown into the Urban Dictionary entry "Caucacity" — with the "c," not the "s":

