There is definite Middle Eastern influence in not only Ala Mhigo's culture and design aesthetics, but also a lot of the ruins in Gyr Abania share similar real-world basis (such as the Ziggarut in the Peaks). Having said that, the majority of Ala Mhigo's population are Highlander Hyur who have a very Gaelic/Norse influence in their naming traditions and society (someone in my FC outright said that "Ala Mhigans are Scottish!" ), so it zig-zags all over the place. And then there is the whole warrior MNK thing with the Fists of Rhalgr which is pure Asian culture.

Like the other nations, SE draws from a selection of real-life ideas, concepts, places and mythologies when world-building so Ala Mhigo and Gyr Abania are no different.