Sorry for necroing, but in case anybody sees this thread, the game is working natively on Linux.
I was scrolling through my games today, saw Arma 3 and got super excited, downloaded it, played it and it worked great!
The only drawback is that it's an older version and on the store page it still doesn't appear as a Linux supported game.
Either way this means that there is a working Linux version and full support is most likely going to come very soon.