I love Dan Pink's wisdom, and absolutely believe in the motivators of autonomy, mastery and purpose, especially for software developers, but I would say that, in this context, the phrase "work harder" is not specific enough.
If you worked for a company and you knew you'd be rewarded for producing some software on the side, you would likely play around with some ideas and put in more of your time. You also might work more efficiently.
You would not be a more productive employee by being better at code or faster simply because more money was offered to you. But you might make a conscious effort and decision to spend more time on your work and less time with inefficient uses of your time.
The studies are useful and accurate, to a degree, but they are, ultimately, somewhat contrived. "Solve a puzzle faster and we'll give you $2" is very different from "any software you build on top of your maintenance work will be rewarded with a percentage cut of sales."
(Slightly off topic...) I'd also say that "autonomy" is an interesting one for me personally. I like having lots of freedom in choosing technology and the process I go through to sort through programming problems and learn new things, but at the same time, I struggle with unclear objectives and goals, ambiguous deadlines and of course, insufficient domain knowledge about a project. I want autonomy of choice, but not freedom to wander the wilderness of a client project, especially when there are so many new things to learn and achieve. So autonomy, yes, but guidance and clarity are helpful in achieving mastery.
Money remains a big motivation factor for those who don't have it.
In general people don't get motivated by what they already have.