http://bugs.winehq.org/show_bug.cgi?id=48006
--- Comment #62 from Sophira wine-bugs@theblob.org --- You know, I had gotten myself convinced that it was a weird issue with my system, and I never actually did solve it. (I had intended to come back to this, but I never got around to it - my apologies.) But I guess now we know that Square Enix do random trials sometimes, so I guess we'll need to be on the lookout for that in the future.
(I'm also kicking myself a little because chances are good that if I had posted this somewhere with high visibility, like Reddit, it's possible that someone at Square Enix may have noticed the Linux incompatibility... but I didn't post there because, like I said, I thought it was a problem with my system.)
In any case, I'm glad the problem is actually reproducible now. In the meantime, I am on a quest to update my heavily updated system, and that's going to take a while, so I probably won't be able to contribute much else. I mostly just wanted to update and let people know that I hadn't actually found a method of working around it.