I see this as a type of psychological manipulation. Almost everyone is interested in other people's story and the basic human trait of listening gets you over that hump. The "and align your request with their self-interest and self-image" part is what gets me. As an off-the-cuff example that someone might use this advice to craft:

“You’re such a generous person. I know you love being there for friends. Could you help me move Saturday?”

It's an example that of course sounds ridiculous to anybody that reads it, but it's essentially what the book teaches. Gather information not even about the person but how the person feels about themselves and then use that as a tool to make them feel good when you're talking to them.

I suppose it's also not helped that many of the people I've met who use this and admire this book have psychopathic traits. They're very good at faking caring but actually can't. It's a cold calculation to them and admittedly it's very effective at getting them ahead.