Aspyr doesn't support mods, so there is no built-in support for mods in Mac Civ5. Hence the fact that you have to hack the software to display the Mods menu option.
Players who have the Steam version can download mods from the Steam Workshop, but only because that facility has to be there to support Windows users, and they don't disable it for Mac users.
Players with the Mac AppStore version do not have access to download mods from the AppStore, since there are none there.
But you may still be able to log on to Steam without buying another copy of Civ5, and then access the Steam Workshop to download mods. I already have a Steam account, and a Steam copy of the software, so I can't test this. Why don't you try it? If a mod downloads, then use the information in the first post in this thread to find, extract and install it in your AppStore version.