Fundamentalists have two problems:
What does the word "fundamentalist" mean to the world? It seems, as the article you have linked points out, that the common meaning of the word is not something that Christians should want to be associated with, that is violence and extremism.
The second problem is the definition of fundamentalism among fundamentalists. In his speech from several years ago, A Fundamentalism Worth Saving, Kevin Bauder pointed out that there has never been a satisfactory, universally agreed upon definiton of "separation" within fundamentalism. All fundamentalists agree that separation is the crux of fundamentalism and is the distinctive that sets them apart from "evangelicals". Yet, I have never read any leader of fundamentalism who has disagreed publicly with Bauder or who has attempted to set forth a workable definition of separation. No one. The sound of crickets chirping is all I have heard. So, we have a movement whose distictive is separation, but no one within the group can define to the satisfaction of other members what it means. That IS a problem.