That's correct. The FAA has one exam each for private, instrument, commercial and ATP.
Both EASA and FAA ATP(L)s are ICAO licences - and both need 1500 hours. You can't just go to flight school and come out with one - you come out of flight school with a CPL/IR. Then you get a job flying for a couple of years to build up to 1500 hours. Then you can think about the ATP(L).
The way I read it, you want to fly big jets without having to take those 14 exams, right? It doesn't work like that in practice. If you get an FAA licence, you'll (most likely) need to live and work in the US as a flight instructor to get the hours. Take the tests and you'll have your ATP - but no jet time, so the airlines in the Middle East won't touch you. If you have the legal right to live and work in the US you could fly for a regional airline for a couple of years, then move over. In short, an FAA licence generally means spending years working your way up to big jets.
On the other hand, if you take the EASA exams, and have the legal right to live and work there - you can start off on a Jet straight away. After a few years you could get your ATPL with plenty of jet time. The advert might say ICAO ATPL, but what they are looking for is experience.