I know I'm mega late to this, but now all you need is a package called Lutris and yes of course the additional 32-bit libraries.
Install Lutris, get an account (free), search "Star wars the old republic" on the lutris website and then run the installer script. You are done!
Well, almost, you of course have to wait for the launcher to update and the game to download
https://github.com/lutris/lutris/wiki/How-to:-Esync
https://github.com/lutris/lutris/wiki/How-to:-DXVK
https://lutris.net/
And different distros will have different ways of getting Lutris downloaded but a quick google search will help you
with that
Or do the sensible thing, run Arch and just pacman -S lutris