We're talking about education, so the question isn't "what's the minimum environment necessary to code?" it's "what can we do to help people learn to code more easily?".
And I agree with the article - a huge part of learning to program is learning how to keep all the important pieces (variables, meanings, program flow etc.) in one's active memory, and learning which pieces are important. In case of a short-term memory "cache miss", which happens way more often when you're a novice, having everything open on a huge monitor makes it much faster and less painful to look up the info you need. Most people have very good spatial memory, so it's easy for them to remember that they "left" a piece of information in, say, the bottom left of the screen. Changing tabs/windows, on the other hand, is an interruption/context switch and requires much more work for the student to find what they're looking for.
It may not seem like much (a few extra seconds and a few wasted braincycles) but this is exactly the type of friction that eventually adds up to a lot of frustration and keeps more people from learning how to code. I could easily see how having a huge monitor and good window placement could be the difference between a student burning out and "making it over the hump" of really understanding programming concepts and taking off.
TL;DR Huge external monitor = training wheels for programmers.