The easiest and most reliable way to make your SWGB support widescreen is to download and install the following patch:
Steam :: Star Wars: Galactic Battlegrounds All-In-One Patch
This patch was released on Steam last month (March 3rd, 2016) and it works great. It even optimizes the game, making it much more stable and enjoyable in single player.
It's great to play SWGB in 1080p, your screen covers a huge area of the map compared to the lower resolutions we had to endure back in the days. 1920x1080 is a great fit!