No: This is ¾ of the/a slogan of/blurb for the tabletop RPG Eclipse Phase, not a quote from Peter Thiel. Eclipse Phase describes itself as “the post-apocalyptic game of transhuman horror”. The full quote is
Your mind is software. Program it.
Your body is a shell. Change it.
Death is a disease. Cure it.
Extinction is approaching. Fight it.
You can see the ...
There is precedent for the first three lines that predate the game, Eclipse Phase mentioned in Antal Spector-Zabusky's answer. A clever game designer put them together to fit their game concept.
Your mind is software
Found this book chapter from 1994: 'The Mind as the Software of the Brain' (An Invitation to Cognitive Science, edited by D. Osherson, L. ...
As of roughly August 2021, per a note on Lemmino's video investigating the origins of Lisa Holst, Snopes founder David Mikkelson has admitted to fabricating the PC Professional article and the writer. Avery's anagram was correct.
The closest information I could find on the matter is from the book The Unknown Capablanca by David Brandreth and Dale Hooper, which contains the following passage amidst the transcripts of some of the games played at the House of Commons (p. 158):
During the display one player tried to put in an extra move, as is the way with politicians; but the Cuban, ...