What he might want to use this power for, is less clear, he is not quite the classic Libertarian people here seem to think he is. He strikes me as more of the Hoppe variety, or even a post-Libertarian ala Moldbug.
If you have a classical education (reading lots of old books) then this is all perfectly comprehensible. The story Thiel tells is also intuitively comprehensible to blue collar workers without being fortified by intellectual assistance. Having both a classical reading library and a blue collar background everything I have seen so far makes perfect sense.
If however you're part of what the WaPo describes as:
"The one publicly acceptable reason seems to be that Silicon Valley needs to become more than an ossified monoculture of liberal upper-class privileged ethnic groups.
“Tech industry is primarily out of touch by being too far to the Left,” tweeted investor Keith Rabois, in a conversation about Thiel."
Then nothing will ever make sense, just as the Remain voters in Brexit literally find their loss incomprehensible. There is nothing wrong with being left oriented politically, it's a perfectly acceptable set of values that society often requires but if you're surrounded by people identical to yourself you're unlikely to get substantive negative feedback.
I have to say that in experience the middle classes are much more resistant to the realization everything is not improving outside of computers despite the evidence surrounding them. When they see troubles ahead they want to shoot the messengers, usually by describing individuals as mentally ill or conjuring up bogeymen like the Nazis, they are extremely resistant to the idea we are dealing with a systemic problem. A decline is not in their portfolio or in their suite of mental models.
BTW, off topic, but this campaign is crazy. I don't like either Clinton or Trump, and have mentioned to friends and family that I will leave the presidential part of the ballot in November blank or vote for Jill Stein. It just seems wrong to me to vote for someone I simply don't like. For this honesty, I have several friends who are all over my case for 'wasting my vote.'