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.
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...
