GIG is mainly a tourist, not a business destination and American has had this route on and off for a few years.
Dutchjet, American has a history of starting then stopping high profile routes out of JFK, even before the new terminal construction began. In 1987, when AA launched transatlantic services from JFK to Europe, it operated JFK-FRA, JFK-LYS, JFK-BRU, JFK-ZRH, and JFK-ORY.
JFK-FRA was terminated in 1989 and then revived in 2000 briefly before being axed again. There was a talk of JFK-AMS. It never happened. JFK-BRU was dropped in 1998. JFK-ZRH was dropped in 1996 and then resumed after Swissair became Swiss and dropped a few frequencies on the JFK-ZRH run. JFK-LYS was short-lived. JFK-MAN was another route that was briefly flown and then stopped. It operated from 1991 to 1993. JFK-LGW is another route that American initially flew when it acquired TWA's Heathrow routes. TWA had a JFK-LGW slot and American initially used it, then transferred it to Newark so it could fly EWR-LHR, a route not covered by TWA.
I'd bet that the JFK-NRT gets the axe before the end of the year too.