That one weird Raen quote from the first lore book about dialects I think is just worded poorly. The second lore book clarifies that while most modern languages are descended from an ancient Allagan language, that Hingan and Eorzean are entirely different languages. But when western traders made their way to the Far East, the "Common Tongue" ended up catching on there and quickly spread. The bit about it being a strange dialect is likely just that - many Domans and Hingans can speak Eorzean Common, but because of differences in localization in the Far East, and the continued use of several Hingan phrases, it comes off as an odd dialect.
I've compiled all the language lore I could find in this post on
Languages and Accents. All of the new EE2 language lore is there, as well as pictures of the new Far Eastern script.