Hm, I would call this a paradox. Or do you mean something like self-reference? Like Epimenides paradox? Epimenides was a Cretan who made one immortal statement: "All Cretans are liars."
Well, in irony, the verbal part (locution) is usually neutral, but the hidden part (illocution) is critisism of the ego of the other. Say "you did it well..." The double meaning, the irony, is the hidden criticism.
In this case the criticism is overt, so I would not call it an irony. Just a paradox of self-reference while learning this sentence.
But of cource it just a question of terminology, nothing important.
DL should accept "you err" as an alternative to "you are wrong". It's not very common, but it is correct, and is actually a more literal translation of "אתם טועים". They should also accept "you are in error", but I haven't had a chance to try that yet so don't know if they do. I reported the first one.
So what? You cannot use to wrong without an object in English, you always wrong someone. If you want to verbalise it in English you would get something like you are erring or you are making a mistake. This still makes you are wrong and you are incorrect synonyms, although the latter might be אַתֶּם לֹא נְכוֹנִים.