This is just...no. It is entirely conceivable to have a world that is always just. Justice is not a zero-sum game. Abiding by the moral principles of right conduct absolutely does not entail that you, or others, must also fail to abide by the moral principles of right conduct.
Similarly, depending on the particular arena, it's totally possible to have black without white (turn off all the lights), plus without minus (ionized hydrogen nucleus), and light without darkness (a room with walls, ceiling, and floor made of luminous material). And even if absolutely every single one of those things WERE in fact truly, inherently dipolar, it wouldn't prove a single thing about justice and injustice--because the argument is inductive, not deductive ("X, Y, and Z are all dipolar, therefore Q *must* be dipolar too!")
This is like that ridiculous "if everyone is special, no one is special"Syndrome spouts in The Incredibles. It's the equivocation fallacy--because two different meanings of "special" are being used. If you actually force a single meaning of "special" the whole idea falls flat--e.g. "If everyone has a unique ability possessed by no one else, then no one has a unique ability possessed by no one else." The only way it works is if it becomes statistical: "If everyone becomes above average by the old average, then no one is above average by the new average." But again, you have to sneak in that "old vs. new" distinction--the two specials aren't the same because they don't refer to the same population data anymore. (And it also overlooks the fact that, by having an average, there almost certainly have to be some people who are below it and above it, because a population that was all EXACTLY at the mean would be incredibly unusual.)
I believe what he is saying is that the concept of justice would not exist had their not been injustice in the first place. That is true. Humans create ideas to fix problems. Injustice was a problem, thus the creation of justice. Maybe not in those exact words until the word was created, but the basic concept is sound. Ideas are discussed because based on observation and analysis of the human condition creating the concepts that we contemplate concerning human behavior.
I don't necessarily believe the analogy applies to a fantasy game. I certainly wouldn't look at someone at a table and tell them "They had a fair chance" in a voluntary game. Injustice and unfairness are usually involuntary. Very few, if any, people voluntarily submit to injustice or unfairness. If you're running a game with point buy and rolling and a player rolls exceptionally poor, he does have the option to find another game until he finds a suitable stat generation method, thus defeating the perceived unfairness.
We're playing a voluntary game. This whole idea of fair and unfair is more a matter of individual perception. No one has to play in a game their perceive as unfair and probably won't no matter how much the DM tries to explain the idea of "hard knocks" or the like.