Ok, so by this definition, Stalin was certainly not left-wing, since he exterminated and enslaved minorities, which you appear to agree is not supportive of social equality. Yet Stalin is used in the same Wikipedia article as an example of left-wing activities.
Also, if pacifism is left-wing, then the Obama administration is certainly not left-wing or anything close to it, since he has repeatedly authorized military action. I suppose you could finesse this point by saying that neither major party in the US is left-wing by your criterion. But trying to apply this more generally, for example to claim that Stalin, Mao, Pol Pot, etc., were not "really" left-wing, looks a lot like a "no true Scotsman" argument.
In fact, by the pacifism criterion, I'm not aware of any government or political movement that has ever been left-wing; the closest thing to it would be some religious orders, like the Amish, who really do try to be pacifists. (Some people would put the Quakers in this category, but the Quakers have always flavored their surface pacifism with a strong pragmatic streak; they sold gunpowder to Washington's army during the American Revolution, for example.) But this makes "left-wing" a basically useless term, not to mention that you would have to explain to an awful lot of people that they have been using it wrong for a long time, since most people apply the term to Stalin, as I noted above, as well as Mao, Pol Pot, etc.
Finally, if left-wing means supportive of social equality for everyone, then once again, there are hardly any true left-wingers and never have been. Take trade unions, for example: yes, they're very supportive of social equality for their members, but are they equally supportive of social equality for management? Not to mention social equality for people who are not members but would like to learn one of the trades that are unionized? In my experience, unions do a very poor job with things like apprenticeship programs, because training new members means less job security for existing members.
Similarly, central planning in economics, which is supposed to promote more economic equality, ends up giving special privileges to the planners and those who are closely connected with them (like large financial institutions); witness the huge bailouts of investment banks after the crash of 2008, while ordinary people got foreclosed on. The closest thing to true left-wingers by this criterion are left-libertarians or anarchists (which, to be fair, the Wikipedia article does mention).