As an avid fan of Elephant Seals and one who always hopes for their return to the much better zoos of today than the past ones from which they died out, I'm pleased to tell you that aparently it is not the only one.
At least one, if not two, parks in Japan do keep Elephant Seals, and one of them may even breed them; at least I have seen photos of a very young one on their website. The problem with getting any further information has to do with language barriers. Actually I have a zoo friend in the USA who has lived there since the 1960s but was born and grew up in Japan. I asked him if he could translate some material from the website of one of them, but he said that the text contained no information of use, only things aimed at children.
Some years ago I asked a friend who was at the time a Curator in a famous Dutch zoo, if he could arrange Elephant Seals for a new marine display that they had planned, he said that, in fact, he technically could, they'd be available from some aquarium or park in South Africa. I didn't ask him about the name of the place, assuming it would not be something he'd be happy to let out, but despite numerous Google searches, I have not been able to find out anything further.
Update: I just remembered that I did communicate privately with an Argentinian member of this forum once if there were any of these animals in captivity in Argentina. He confirmed to me that in addition to Mundo Marino, there is also the Mar del Plata Aquarium. Furthermore there is also the possiblity of the occasional place in Chile and Uruguay holding this species.