Square-Enix actually have a bunch of games on the iOS App Store. Most of them are ports, but a while back there was the Chaos Rings series which was original IP (I haven't checked if they have any other original IP for iOS). And they're not just straightforward ports either, for example the Dragon Quest games have all been adapted to play in a portrait layout (because their target customers are Japanese people playing while standing up on subway cars, where they can't do two-handed landscape gaming).

I also find it notable that Square-Enix is maintaining relatively high price points for these games (such as $15), and have done so for years, despite the iOS game market still being primarily aimed at the $1-$3 level. Of course, the fact that the games are being published by a well-known name like Square-Enix lets them do things other companies couldn't get away with, but it must be profitable enough because they keep adding more games to their iOS lineup.