XIV is loosely based on 15th - 17th century cultures, plus any "anachronistic" technical advances made possible with magic and magitek (such as the early propagation of things which, in the real world, stayed on their original continents for much longer - for instance, I'm going to say coffee is likely to have been invented somewhere along the Thavnairian archipelago, which we know Eorzea has active and open trade routes with).
Most of these foods were either invented thousands of years before then, or were invented during the time period XIV is based upon.
Just because they've become modern conveniences doesn't mean they were invented in modern times.