It stands to note that the Japanese version of the game has the Doman/Hingan characters speak in a different, older dialect of the Japanese language. This was noted as far back as the first Ninja quests by a friend of mine who plays the game in Japanese. Essentially the Japanese version of the game assumes all "languages" are just different forms of Japanese. This is also likely the reason for the possible translation error in the lore book which refers to Domans speaking in a different "dialect" rather than a different language altogether, which has now been contradicted by the lines posted above.
For all intents and purposes I am inclined to think Hingan and Doman are both actual and presently used languages within the localization. The reasoning behind everyone speaking the common tongue is fairly simple...in Kugane it's a foreign port, the common tongue would be incredibly useful. In Garlean-occupied Othard the common tongue would be taught and spread as a means of gentrification of the region (we see the scene where young Yotsuyu's mother wants her other child to have the best in Garlean education for example). That and on an out of universe level the English language, though diverse, doesn't exactly have a similar version of 'dialects' like the Japanese language does so it made sense to change it from simply a dialect to a full-blown language.
For all intents and purposes I am inclined to think Hingan and Doman are both actual and presently used languages within the localization. The reasoning behind everyone speaking the common tongue is fairly simple...in Kugane it's a foreign port, the common tongue would be incredibly useful. In Garlean-occupied Othard the common tongue would be taught and spread as a means of gentrification of the region (we see the scene where young Yotsuyu's mother wants her other child to have the best in Garlean education for example). That and on an out of universe level the English language, though diverse, doesn't exactly have a similar version of 'dialects' like the Japanese language does so it made sense to change it from simply a dialect to a full-blown language.