I would disagree but I can understand why some ppl might think that these days.
There are many things which either originated or are more prevalent in Asian role playing games. The upbeat atmosphere, cinematic story focus and extensive cutscenes, class switching, weapon bound classes, cute fodder monsters goblins/slimes/spriggans/mushrooms/etc all look very different to western concepts of those monsters, cat girls, chibi style races =/= hobbit style halfling, heavy focus on emotional character emotes. It's also true that WoW popularized more bombastic attacks, armors and weapons in western games but that doesn't mean it's no longer a hallmark of Asian games.
Final Fantasy is also quite self-referential as a series and constantly builds on what was done previously. The first was mainly referential to Dungeons & Dragons at the time which drew from a lot of Asian influences for cosmological design during that time period. It was only recently that Dungeons & Dragons started to base designs on more biblical concepts and influences from other games. In those older days many of the Asian influences came from mythology borrowed from the middle east, India, China, Japan, and some others, especially their concepts of astral planes and karmic beings.
Just consider some primal names off the top of my head bahamut (arabian), ifrit (arabian), garuda (hindu), shiva (hindu), leviathan (semitic), behemoth (semitic), ravana (hindu), lakshimi (hindu), susano (shinto/japan), zurvan (zoroastrian/persian), sephirot (semitic)
The European aspects are generally Mesopotamian or Norse in nature. I don't think there will ever be much that originates from Celtic or Germanic mythology. You can point to concepts of classic swords and armor but even the real Damascus Steel used Wootz/Ukku/Hindvi from India, and the process has been lost for centuries and never reproduced even today. Damascus itself is the capital of modern Syria today.
The world is far more cosmopolitan than almost any western game but doesn't suffer from tropes of Orientalism.