My definition is roughly "ability to process information and generate useful conclusions as a result". Rationality would be a "side-effect" of intelligence, not part of the definition itself. I think that it's more useful than the def provided by the author because sometimes intelligent people with dumb beliefs will also do dumb shit, that clearly contradicts their goals. Does that mean that they aren't intelligent to begin with? Acc. to the author's definition, yes.
A good example of that would be Steve Jobs. It's hard to claim that Jobs wasn't very intelligent (even if I don't like him); and odds are that "to survive" was one of his goals. Then why the hell would he prefer alternative medicine over actual medical intervention, for something as serious as a cancer? (It's just an example, mind you, we could use others.)
However, once you shift the definition of "intelligence" to the one I'm using, there's no paradox: he was intelligent, sure, it's just that his "processing ability" was not directed towards that specific goal. And sometimes it might've been directed against the goal.
It's like something is diverting that processing ability from the personal goals to something else. Dawkins' memeplexes might be the answer here: the memeplex "alternative medicine" was competing with the goals of the individual, and leeching off his processing ability to its own end, like a parasite of the mind.
So, alternatively, and in addition to what the author said, we get another line of thought: sometimes smart people have dumb beliefs because intelligence does not immunise you against parasitic memes. Perhaps it even makes you more vulnerable, as those memes will be abler to successfully reach you. And then, [this point agreeing with the author], once those parasites are installed, they'll divert your intelligence towards their goals.
[Sorry for the wall of text.]