Thank you for clarifying.
Regarding the first point, about women being higher in neuroticism, the author does provide a source - wikipedia. I understand there are different versions of the document, some of which omit sources or links. The version I'm using as a reference [1] maintains a hyperlink to Wikipedia's page on sex differences in psychology. Wikipedia may not be the most reputable source, although I've always thought quite highly of it, but in this instance, Wikipedia, which does seem to support the author's contention, has it's source, an academic psychology paper. The paper's abstract [2] does also repeat the Google author's claim, that women are higher in neuroticism.
As far as the Google author's sourcing goes, I believe linking to a well sourced article on Wikipedia should be a sufficient citation for the document (which wasn't intended as an academic paper but something more like an argument on a forum - per my understanding).
I don't see how this claim, that women are higher in neuroticism, leads to what you alleged the author was claiming - that the biology of women hurts productivity at Google. This seems to me like a possible explanation of why there are not as many women in leadership positions, and not an argument that the women who are in leadership positions have any defect.
By analogy, suppose I was asked why there were few Chinese basketball players, and I answered that height is useful in basketball, and Chinese people are shorter on average than white and black players. This may be a suitable explanation for the observed phenomenon, or it may not be, but either way you should not interpret me as claiming that Yao Ming is a short person.
For your second point, this seems obviously true. The "false negative rate" presumably refers to when candidates who would be good hires are rejected for some undesirable reason. In other words, the test is generating an incorrect negative (your interview comes back "Do not hire" on a person who would make a good candidate).
This false negative rate effectively "raises the bar" to get hired at Google, albeit in an undesirable way. The initiatives that the author links to in this section are presumably aimed at reducing the false negative rate for women, and thereby lowering the bar that women need to clear to get hired.
Obviously it's a good thing to reduce your false negative rate. You get more qualified employees and people who are qualified get a good job. The discriminatory part of this, which the Google author is highlighting, is that Google wants to reduce the false negative rate FOR WOMEN and isn't applying these same initiatives to hiring in general.
I agree that the author did not have enough regard for the social context of his post. He seems to have believed Google's lies that they cared about letting employees express themselves and share ideas to improve the company - when, of course, Google is a soulless corporation that will fire anyone with the temerity to criticize their sacred cows. I think that says roughly that the employee was a bit naive.
[1] - https://www.scribd.com/document/355823379/Google-s-Ideologic...
[2] - http://doi.apa.org/buy/2001-01642-012