I think this was probably used as a reminder of "you're no longer a member, Brexit means Brexit", but I think it's in the interest of EU members to assert once again the importance of international law and basic common sense. Argentianian claims are totally baseless of either and are pure expansionism.
PS: And let's not forget that Falklanders were not allowed to vote on the Brexit referendum.
The EU in this case it's, as most of the times, the ensemble of its national government leaders. In itself the declaration means nothing and was probably used as a bargain cheap for Argentina to delay its idea of joining the BRICS (according to some news).. if that was the case it was not so bad, a meaningless declaration in exchange of limiting Chinese and Russian interference in South America, not so bad.