I'm going to take the outre position that both gender and class discrimination are bad.

The differences in callback rates were not statistically different between the women and the lower class men. The only statistically significant different was higher class men and everyone else.

I didn't do the stats on it, but just looking at the graph in the article 5 times as many lower class women received callbacks than lower class men. What was the p-value on that?

Instead of "5 times as many" look as "a difference of 4 samples" - in an environment where the expected sampling noise is something like +/- 4.

"Statistically insignificant" means just that - this data is not sufficient to conclusively say if lower class women receive less callbacks than lower class men; maybe they do, maybe they don't.

Does that criticism make sense given that the title of the article and opening paragraphs talk about the class disparity, and only get to the major gender disparity in the middle of the article?

I'm not the person you're replying to, so I can't say what they were thinking when they wrote their comment. I'm choosing though to read their comment as referring to the larger social context, rather than this specific article. I would note however that this article is classified under the category "Gender" in the Harvard Business Review.