The Middle East didn't stop existing after Ancient Times.
Misirlou is probably from the 1920s, or about 45 years before Dick Dale recorded it. It was Ottoman, at least, perhaps Maghrebi. But decidedly a modern piece of music.
Here's a modern piece of music that turns out to have equally Ancient Origins! https://www.youtube.com/watch?v=V2mb1vgNg70
https://noc.social/@todayilearned/114931889896223598