The original is theirs, the translation is a derivative. Since it wasn't commissioned it's not a work for hire, so the original holder has no right to it.
Granted, I'm no copyright lawyer and goooooogle is not that helpful (half the results are google translate, the other half are legal ways to do this or if it's legal to translate stuff without permission >_>), but wouldn't it be akin to theft if the original owner took the work the translator put in without remunerating it?
To be clear I'm not saying that the translator has a right to disseminate the work, just that without their permission no one else can use it (which means that without a compromise no one can use the translation)
Using US and Japanese copyright laws as a reference, derivative works do infringe on the original authors rights under US copyright law. Meaning in the US as an example, a Fan translation is in essence illegal unless sanctioned by the creator.
Now more relevant to this case would be Japanese copyright laws. The original author is granted several rights. Broken down into Moral rights and Economic rights. Economic rights are more important here, specifically the "Economic right of adaption" which states as follows roughly translated from Japanese to english " The author can control the adaption of a work through
translation, dramatization, cinematization, and the creation of derivative works in general."
Long story short fan translators do not own the translation unless sanctioned as per japanese law the developer of a game controls the right to translate said game. Yes, laws will vary from country to country however I would imagine most countries are going to side with the developer if it went to court.
I will add that most fan translations do not illicit a need for the developer to waste time going after them, but talking legal terms exclusively the law is pretty clear fan translators do not own intellectual rights to game translations unless sanctioned by the original creator.