First, before I start properly, allow me to pose at least this much of a thought - perhaps Aatrox is ambidextrous? He can fight just as well with his left arm as he can with his right (although it seems that most of his power comes from his right-arm, so he holds his sword in his left occasionally to free up that good arm.)
But, beyond that, there's sort of another thing that aught to be pointed out (it's a bit of a gameplay thing, but it's still relevant), and it's that Riot seems to have moved Aatrox away from being a Diver/Skirmisher hybrid to being a full-on Juggernaut. And, it's important to note that he was (and still is, since the GPU isn't live yet) a Skirmisher.
Skirmishers have a pretty distinct fantasy that they embody through their gameplay - being able to step into a fight, tear down their opposition, and step back out alive. And most of the Champions who presently are Skirmishers (Fiora, Jax, Master Yi, Riven, Yasuo, and Aatrox) are displayed as masterful swordsmen/warriors who can turn blades, move swiftly, and fight with haunting, horrifying grace. (the only exception of course being Tryndamere.)
That sort of fantasy (unparalleled swordsmanship, deft blade-weaving, and mastery of arms) usually lends itself to more fluid-moving combat (Yasuo's drifting to and fro in fights, Fiora's impeccable dueling skill, Master Yi's rapid bladework), and consequently, when (and while) Aatrox is classed as a Skirmisher, it makes sense for him to bear his sword in his left arm over his right. It's unadorned, unarmored, and capable of its full range of movement, allowing him to actually do all that blade-weaving and swordsmanship he's known for.
But, post GPU, Aatrox looks to be a Juggernaut - a subclass of Fighter known for being hard to kill, easy to kite, and capable of hitting you like a truck on steroids. And, as he uses a more inflexible greatsword now, he much better fits the class fantasy of Juggernauts - massive warriors with hefty weapons who can bear down on you in force. (Darius, Illaoi, Garen, Nasus, Yorick, etc.)
But, that sort of fantasy demands a different look than the Skirmisher fantasy - he needs to look strong, like every swing is going to shatter armor as well as it would cleave through throngs of men. Like how Illaoi is a large, imposing, well-built woman carrying a massive golden idol, or Darius is a staggering, daunting warrior clad in iron armor and bearing a massive greataxe.
Perhaps increasing Aatrox's size and his weapon's size alone would've been enough, but, it would've still lacked something, and Riot seems to have found that switching his sword-arm lends well into the Juggernaut fantasy. I kind of agree. The chitinous plates on his right arm look restrictive, but, in the same turn, they look powerful. They look as if getting even one hit by them would be enough to send you flying several yards, while his left arm looks like it would send you stumbling backwards a few yards.
I do agree that it sucks that they didn't translate his semi-iconic left-handedness into gameplay, but at the same time, I understand that it's actually kind of fitting for him to use his right arm now. He's not a swift, graceful warrior - he's a killing machine, a colossal embodiment of carnage. They want him to look like he's going to crush you and your army - and having him hold his sword in the more heavily-armored arm suits that purpose.
