It may be true that Thiel doesn't believe one of the three things dragonwriter listed, however:

1. The quote being discussed doesn't require this.

2. If Peter Thiel doesn't like democracy (and therefore would like no one to vote) it would be misleading (although technically accurate) to describe that as Peter Thiel not wanting women/minorities to vote.

If you want to interpret what Thiel says then you have to take into consideration everything that he says. So yeah, the quote being discussed does require this. That would be the case if you consider Thiel as some sort of libertarian intellectual. If he's just a whatIsaywheneverIsayitmeaningwhateverIwantittomeanwheneveritsuitsme-arian then I see your point.

Way to ignore half of my post.

It is completely reasonable to take context into account when doing this sort of interpretation, but it is important to be explicit about what context is included in the analysis. The article we are discussing is being criticized for being dishonest in this regard, which is why the distinction between "implied by this quote" and "implied by something else he said" is important.

I apologize for ignoring the second half of your post. In addition to it being some form of rebuttal, it contained 5 negative clauses. Basically, I couldn't figure it out and thought best to leave it alone.

I guess the idea is that the "tyranny" of the majority would curtail your freedoms.