If you are doing UI stuff that does graphics dual screens are very good. On one screen the debugger, and on the other screen the target application. That way you can debug each drawing step.
For Windows paint event work non-overlapping windows are practically a requirement - if you let another window on top of the one you have paused in the debugger, the OS will draw over it and lose the current paint state.
Then there are scenarios which require two screens on two machines. With "synergy" this can be really seamless with one keyboard / mouse.
That's the first time I've ever seen someone else mention "Synergy"
I used it back in college When I had a spare laptop I wanted to use as a second display. It seemed like it was doing really hacky things behind the scenes but was probably the easiest instance of "Software Remote KVM" I've ever seen.
Synergy is still around, and still works remarkably well. The mouse scrolling between OSes is a bit janky still, but still something I can use every day.
Furthermore, full screen, maximised browser is the default and how the customer will see the page. So you want your debug tools in one place and your target browser experience in its own window on its own screen. This is totally valid 1366*768 is probably the better target resolution for regular sites. You also need a real phone to develop on too.
I do agree with the author but not all use cases are the same. You could not apply this workflow to live editing of a football match where a gallery has scores of monitors.
Work is also collaboration and two monitors helps. You can explain things in a show and tell.
