Earlier quoted context omitted.
I can imagine this being more helpful if you lacked access to a debugger, and lacked the time (or desire) to build debugging tools by other means... Which I imagine is plausible in that context.
No, they have debuggers and modern dev tools. They just prefer to read code from paper when they have to really focus on it for a long time.
In my experience, it's less about reading code on paper than it is the other thing you mentioned:
>then they annotate it with a pen while thinking about whatever problems they are solving.
Paper and pen offer a lot of options you don't have in vim (or emacs/notepad.exe/etc ;)). Circling, doodling, arrows, underlining, furiously scribbling...