First of all, the introduction which bashes the paper which applying social network techniques to fiction? If the author had bothered to look it up, they would have realized the authors are an applied mathematician and theoretical physicist. Not humanities.
Then they goes on to criticize political science and psychology as their poster children for the humanities, except these are social sciences, and only "humanities" in a very broad umbrella term. "Humanities" is more often used to refer to disciplines such as history, art, literature. So a complete mix-up of fields.
Third, the assumption that social sciences has a "reliance, insistence, even, on increasingly fancy statistics and data sets to prove any given point" is simply flat-out wrong. For example, of course political science relies on "big-N" studies which try to find or refute correlations between democracy and various other country indicators. But political science also relies heavily on "comparative politics" which is much closer to literature or history in a classic "compare and contrast" aspects of two countries. Similarly psychology has many different approaches taken in published papers and books, some quantitative and others more qualitative.
I could go on and on. But this article is completely ridiculous, arguing against a straw man that simply doesn't exist. It's like the author isn't even familiar with academia. Bizarre.