"Dialectical" in the Marxist sense can best be described, I think, as a sort of "force" of logic. Dialectics in and of itself is simply a form of conversation between two people wherein each posits ideas and theoretically, on average, the more logical ideas will influence both people and become their de facto stances, if that makes sense.

Marx took this concept and applied it to the material world - dialectical materialism. The thought being that when two forces, say countries, interact with each other, on average, the one that would most "logically" prevail in the interaction, be it diplomatic or adversarial, will be the one that does prevail - usually because of some technological or material advantage. This seems obvious, but the starkest contrast to it would be crusaders who got their asses kicked in the Crusades. They didn't pursue a materially advantageous war. They fought because of idealism - that their god was stronger. And people to this day will fight "idealist" wars and lose because people don't always consider their material conditions.

It has therefore become common among Marxist, and leftists in general, to refer to things that prevail because of their logical "force" as being "dialectical." Which is to say, the reason that the thing, be it a country, a word, or anything really, is successful is because it has a logical weight behind it that propels it pass other solutions.

So the above poster calls "y'all" dialectical because 1) it is probably a pun because y'all is commonly said in certain American English "dialects" - such as in the South - therefore it is literally dialectical and 2) because y'all has become so prevalent, despite being derided by language purists, because it is such a functional term for the English language. The language purists are "idealists" who fight to prevent impure language from becoming prevalent, but they are clearing losing out. The reason for that is that there is a "material" advantage to having a plural second person term - it saves time and effort, especially now that we see an increasing need for gender neutral terms. And so, since the material advantage of having an "impure" second person term is prevailing over the "idealist" stance of keeping the language "pure," we can call this phenomenon of the word "y'all" becoming prevalent "dialectical." The logical necessity for such a word allows its usage to become standard even in the face of constant push back from other ideas.

That said, I'm all for it becoming "surfer lingo."