Sure, at times, things can get downright stupid with what people use the courts for, but I honestly feel he's justified to get something. Part of the idea of punitive damages is a way of using money to tell the guy who's wrong not to do it again. It's not awarded because the guy who's suing them deserves it, but it's there to punish the asshole for whatever they did. Suing someone and using the "emotional distress" stuff is essentially the same deal as punitive damages. It's there because sometimes what people do to get sued isn't technically illegal, however, it still caused a lot of trouble for the person.
The whole point, though, is that things have gone beyond simply calling him names or something, it's gotten bad enough that he is willing to leave the job because of it. Obviously, being called names isn't fun, but if it's simply being called names by someone, that's one thing, but having someone (even worse, in Itagaki's case, since it's his boss) going to the people you work with, who are supposed to take orders from you, and talking behind your back, along with essentially turning the people you have to work with against you can be a major issue. If any of the employees working under Itagaki agree with Yusada, and say things to Itagaki's face, that undermines his authority, along with creating unnecessary stress, and reducing productivity. Essentially, Yusada has made Itagaki's job hell, and Itagaki is fighting back.
Just because you can't really do anything about it most of the time, doesn't mean that it's right. Just like bullying in school, in the grand scheme of things, it's nothing big, but it can be bad enough to make kids go insane and shoot up their school. Obviously, younger people are more vulnerable to bullying and such, but it's never fun to be bullied, and there are few times when anything CAN be done about it, so when there is, why not take it? Why not make Yusada think again before he opens his mouth and says something insulting or offensive about someone working for him.
Hell, Itagaki might have been able to charge Yoshimi Yasuda for harassment or some other such crime, if he really wanted to.
Of course, most aspects of harassment require actual mental or physical injury, but that is somewhat mitigated by the fact that they already have a reason to sue, in cases like Itagaki's.