[The Might]

I agree...I always found it funny that Gandalf makes some Jedi style hand move after Aragorn turns around...and then of course the famous "For Frodo!" line.
Anyway, there is no way Aragorn could have seen Barad-dur from the Black Gate anyway, that's just changed in the movies to make it look better.
However, we do see that Sauron is summoned to come to the Black Gate as well, so this "Aragorn, Elessar" thing might be seen as a reply to that challenge.