In the interest of brevity I probably wasn't specific enough in my comment. There is of course tons of scientific credence to the idea that different areas of the brain are specialized for different functions. I have not read the work you are referencing, but I suspect the author cites science that addresses this localization of brain function. What he can not have done is reference reputable scientific sources that take the next step and assert that individuals are "left-brained" or "right-brained" due to increased activity on that side of the brain resulting in exaggerated personality traits. He can't make such references because they do not exist, to my knowledge. Correct me if I am wrong, please.
This is a beautiful example of new age pseudoscience. A layperson takes some actual science and then draws his or her own conclusion from it. Just because their source information is accurate does not mean their conclusion is. These people need to be called out as frauds, not lauded and given TED talks.
TL;DR: Specialized functions in certain brain areas: real. Individuals being right- or left-brained: not supported by any known evidence.