I've been seeing folks get excited about this, and haven't yet been able to see why it is so interesting. However, the people behind it (Bret Victor et al) and who I've seen playing with it are too interesting for me to ignore this...
I do very little of my coding on a computer. Instead, I build up all the discrete parts of my code using sticky notes, that kind of get constantly re-organised while I'm writing.
So my desk ends up as a mess of sticky notes that get pushed and pulled around, which seems a lot like what you can do with this - except you can also run each part of this code, instead of relying solely on your memory.
Of course, it's nothing groundbreaking just yet, but I can't help but get excited at the possibilities of this sort of medium.
So even when playing just with the papers, you can be programming.
You can sketch a UI element on the paper (eg a rectangle and token for a numerical slider), then go back to code the interactivity. Units in the code are inches on the table. Subtle things like that break you free from the laptop.
When you want to "commit" your code changes, you print a new version.
IMHO, the ability to create new physical interfaces to editing code might allow for new programming paradigms to pop up, or better interfaces for people to develop logic in their own domain. Someone could combine a calculator interface and a context-sensitive variable selection interface to write arithmetic logic using an interface/"syntax" that they already understand, and debug all the way through that with a testbed program that allows the programmer to set variables to specific values and work through how the math works. You can have yet another program which describes a program as a flowchart and allows people to edit it that way.
The thing is, as you make the IDE physical, you get to invite people to interact with it more - rather than staring at a screen, suddenly you're livecoding, you can have multiple people working on it at once. "Ah, but doesn't that fail if you do this? Sets some variables on the testbed", or "I can fix the UI while you update that calculation".
And then, when your accountant has something on a piece of paper that works, they could point a "make this an app on my computer" program at it and bring it out of Dynamicland, into their workplace.