On their way to Cyllage City, our heroes meet Nico and Chester, two brothers who introduce them to the incredible Battle Chateau. Its owner, Lord Turner, explains that the Trainers who battle there are considered knights and expected to adhere to the knight’s code of chivalry and honor.
As you said, in the Anime it's Turner, and there isn't really anyone who 'owns' the Battle Chateau in the games, so I think it is safe to say that the owner of the Battle Chateau is Turner.
The strongest regular trainer in the game though, is Henessy, his Pokemon being at level 50, and he also gives out the most prize money.
Also understand that the Anime and game can be very different, so even if something in the Anime is different from in the game, then it isn't exactly wrong.
