Chile turned from a communist shithole into one of the most prosperous countries in Latin America because of laissez-faire policies. Technically they followed the Chicago School, not the Austrian, but they basically followed the same principles: cutting taxes and tariffs, de-regulation, privatization, less welfare, low inflation etc.
I think most people are missing his point. The people can be economically freer while not being politically free. If you did not get on the governments bad side and were a free market business, you would do better under Pinochet. This does not make that business man bad. I guess people say the same thing about China today. They are not politically free but economically freer and standards of living depend more on economic freedom than political freedom.
His point is more subtle. If you wrote angry things in news papers about the government, things would suck for you a little more under Pinochet, but if you were a free market, very productive person that stayed away from the government sector, things would suck for you under Allende. The government was more likely to come and take your life's work.
The simple "Pinochet bad... so Allende good" is a bit too simple.