> If women should not even have the vote, why should we worry about gender diversity in the engineering ranks?
These two paragraphs read as a microcosm of this whole episode. Think what you may about Peter Thiel, but the quote does not say or even suggest that "women should not even have the vote." It merely points out that as the voting public has been broadened, it has been broadened to include sectors that are not (historically) as amenable to limited-government policies. Therefore, the relative popularity of limited-government policy among the totality of voters has diminished, suggesting that democracy and capitalism are presently at odds. Reading the quote with a reasonable level of charity suggests Thiel would prefer to convince these voters of the appeal of limited-government policy, not revoke their right to vote. Simultaneously, he is also presumably arguing, as many others have, that simply increasing voter turnout does not necessarily lead to better governance.
Can the New York Times point to any quote from Thiel that justifies the implication they have made here: that Thiel believes women should not have the right to vote? Perhaps there is one; I really don't know much about Thiel. But this quote alone isn't it.