The act itself isn't a racist one. Racism isn't about words. It's about how you view other races. This particular woman made it clear she is racist, but not just because of her saying "nigger". I've had people call me "nigger" before plenty of times growing up. You can tell those that say it just because they want to really piss you off and those that actually view you as a "nigger". It's much like calling a woman "a dumb bitch" because you want to upset her as much as possible, not that you are actually sexist and hold a lower view of women.
Just to be clear, the woman is a racist or clinically insane. Assuming she doesn't talk to every single person like this, It's obvious that she is racist because her entire attitude is towards him was predefined by his race. She was upset because he was a black person. I just think that distinction is important because in my eyes, the part of racism I want to be reviled the most is the fucked up views people have, not the words.