Sorry... I am an oldtimer... WINE is of cause a emulator.
Except that WINE Is Not an Emulator
It's a bridge between Windows application and system libraries and a native OS such as Linux, Mac OS etc., which lets you run Windows app as if they were native apps to your system, with various limitations of course.
Anyway, I'm not sure if the installer works under WINE, I know it doesn't under Mac. You might want to try downloading doh123's Mac wrapper for STO as it includes the STO launcher ready to update itself and download the game. On Linux it should just appear as a folder which you can open to find its C drive contents. Copy the STO Program Files folder into your WINE install and try from there; the launcher should hopefully update itself and download everything you need to play STO.