Although the whiteboard is good for some purposes, the author specifically mentions "brainfuck" coding questions.
Having them do those on the whiteboard really only tests how the think on their feet in high pressure situations... Something not really required of 99% of coders.
White-boarding in a high pressure situation is simply a different "skill"... I think it's fair to say that most coders are "internal" thinkers / introverts, that do their best work when they have a chance to quietly think about a problem.
On the whiteboard, you're asking them to do the exact opposite.
Eliminating the "brainfuck" white-board questions doesn't mean you need to soften the interview. You can actually give a more substantial take-home problem to your final round of candidates.
But, I'm biased. I would never do a take home interview shrug
Though as my first job was at a RnD Organisation this was expected from everyone from the shop guys to the Boss (the then president of the mechanicals) I might have a higher expectaion than most :-)