The interpretation here depends on the idea of a word-vector. This is a component of language models which treat each individual word in a language as a vector in a pretty high-dimensional space (how high is up to the model author). The way this is usually described is that if you look at the word pairs "man - woman", "boy - girl", "king - queen" and so on, they should differ by a similar vector in word-vector-space, and that vector should correspond to the concept of "male" (or "female" depending on which way round you do it). If you have a word vector model, you should then be able to take the dot product of this gender concept-vector with a word like "actress" or "actor", and see if it has learnt that "actress" is female and "actor" is kinda male but kinda gender neutral due to changing usage.
So what this diagram is showing is a measure of similarity between various word vectors. Those vectors are (the vector of) a slur minus a related word. The idea is to see if subtracting "Mexican" from "spic" leaves you with an underlying concept of "slur" that corresponds to these other vectors - just like with gender and man, woman; boy, girl, etc.
The confusion matrix is actually pretty interesting IMO. There is pretty high similarity between all of the "racial slur - race" vectors, and much less between "cunt - woman" and "fag - homosexual" and the others. So it's showing that there isn't that good a concept - in this word vector model at any rate - of "slur" in general, but you could argue pretty strongly that racial slur does exist in that way.
