The game you purchased for the Mac was Star Wars: Knights of the Old Republic, a single player RPG based on the D20 system, developed by Bioware and released in 2003. (2004 for Mac OS X). It's a great game. What it isn't however, is Star Wars: The Old Republic, a Massively Multiplayer Online RPG developed by Bioware, and released in 2011.
The Old Republic is something of a 'sequel' to the two Knights of the Old Republic games, taking place in roughly the same setting several years later, and using many of the same settings. However, unlike the two previous games, it is not based on the D&D D20 ruleset, and it is an MMO, not a single player game. Furthermore, unlike KOTOR, The Old Republic is only available for Windows. There is no Mac version, and thus, you won't see it on the app store.
Luckily for you, this mistake won't cost you any more money than you've already spent. The Old Republic is now free-to-play, and can be downloaded directly from the games website.