You're trying to defend a pejorative by using an absurd caricature as a straw man stand-in for people who actually support justice. It is pretty weak sauce. I mean, think how awesome and powerful Justice must be that you have to pretend it doesn't exist in order to argue against people who support it?
Justice and Social Justice aren't the same thing. One is intended to right a wrong, the other is intended to make everybody the same. While that might sound good, it often results in knocking people down just for the crime of being successful. When taken to an extreme, (such as an SJW) it results in the examples I listed, and instead of bringing down successful people, they come down harshly upon anybody who happens to make an ill conceived but otherwise benign action.
You even throw in a True Scotsman for good measure
Not at all. I very clearly outlined what it is, in my own opinion. To pull a "No True Scottsman" fallacy you have to create a definition that can never truly be met.
Do you even comprehend that you're fighting for perceived social justice in your argument? What is an "SJW?" People who do as you do here, and make a case for social justice. You can't be against bullies, and admit you are, and not be a social justice warrior.
No, that falls under justice; that is, righting a wrong.