The video talks about how monetary rewards only improve performance up to a point, after that it can even hurt performance. While autonomy, master and purpose do improve performance:

This may imply a counter to Austrian economics, I'd like to explain why it's not.

Opportunity cost

This aspect of choice is ignored by the experiment. When people engage in a scientific experiment they've already decided upfront that they're going to spend time on the experiment. While in normal life you can only do one thing at a time. You either take this job or another job, you spend time with your family or at work, do work you like, accept discomfort and many other choices. In normal life more money does motivate people to take one job over another.

Gender influence on work choices

These influence appear when people start having children. Before that men and women are very similar. Warren Farrel documented at least 25 choices men and women make differently after they have children. Men in order to make more money, women in order to spend more time with those children.
Why men earn more - by Warren Farrel
So even if more pay degrades performance, it's still a way for society to get people to do job B if it brings more value than job A. Job A might be more enjoyable but less valuable for society.

Mechanical tasks are affected by pay

So this suggests that the reward does affect incentive.
So maybe there's something else going on with the more complicated tasks.
Like the higher reward causes people to overthink things.

Questions about setup

There's no link to the original research and I haven't been able to find it.
I wonder how the experiments where setup.

The people offered the top reward did worst of all
So did they split people up into different groups of people and offer them different amounts of money for the same task?
Or did they take a single group of people and tell them they'd get one of three rewards based on their performance?
I'd be really interested to see how these experiments where setup.

autonomy, master and purpose

All of these aspects are improved with economic freedom. It allows for capitalism, which improves our productivity to such an extent we have more free time to do things we want beyond the day-to-day survival stuff. Go on vacations, do scientific research, follow our interests, improve our skills, do work in line with our ideology. We can see this in stats, the more economic freedom a country has, the better quality of life gets. Including things like environmental quality. Environmentalism is a luxury people in the west can afford because of capitalism:
https://www.flickr.com/photos/shanedk/sets/72157646459874723/