My theory about thinking and walking is that it gets the blood flowing round the brain more than just sitting at a desk does. I think that was the thinking behind having table tennis tables in offices as well, to get the blood moving around. There's also something about the action of walking that seems to let the mind wander off as well though...
For example, I'm pretty bad at creative tasks when at a keyboard (this was also true in pre-internet times, so it's not a matter of distractions), but sit me down with a pencil and paper and the juices start to flow. It just creates a different state of mind.
I tried to replace pencil & paper with minimalist emacs buffer but .. paper is non linear, just like thought trails so it's a better fit for now.
Lunch dragged on for a couple of hours sometimes, but I generally had a flexible enough schedule that it worked ok.
With IDE's, Photoshop, Word, I think it's important to remember that they have activities and workload in themselves that isn't relevant to what you're trying to achieve. Separating this load out from the core task has some value.
Something like mindmapping over a code printout that could be exported back to your IDE or text editor via a plugin, maybe.