I usually recommend using a fresh WINEPREFIX for every new application installed with wine, as that very often eliminates problems that using the default ~/.wine folder with everything can cause. Nevertheless, so we can get an answer for this question, here's how I installed it on Ubuntu 12.04, which was largely a similar process to that very briefly mentioned on the information page at WineHQ. It may well be available on Steam in the near future, but that is just surmise.
Star Wars Battlefront 1 can sometimes work on wine, but often there are problems or glitches with the graphics, so it depends on your particular setup and version of wine as to if or how well it will run.
