Aren't you using your own version? The original meaning of left and right is the French Revolution, where people who sat on the left wanted revolution and people who sat on the right wanted to keep the status quo. People who sat in the center wanted a little bit of both. Then the definition transitioned to left being collectivism and right being capitalism.
But for some reason a good portion of academia (to not say most) labeled right as authoritarian and violent, and left as humanitarian and progressive. Hell, even Wikipedia and Google definitions says that national socialism is a far right-wing movement. So I don't blame you, definitions are a bit messy
I'm using the common version. It's not that the right is authoritarian and violent and the left is humanitarian and progressive. It's that extremes on both sides are authoritarian and violent, but differently. (Nazis vs Communists being the obvious example there.)
I actually think the 2D version discussed in your link makes a lot of sense overall. But I think it's a mistake to label the horizontal axis as "Left/Right." Just label it "Collectivist/Individualist" like the vertical is labeled "Authoritarian/Libertarian."