The source-code to the original Doom 3 game has been around for much longer than the Doom 3 BFG code but there hasn't been much activity with it to date and most open-source games out in the wild are using the older id Tech 3 (ioquake3) engine. However, having the original Doom 3 Linux-compatible code out there made for easy porting of Doom 3 BFG to Linux.
I wrote last December about Doom 3 BFG having been ported to Linux. The most notable community-based project is the "RBDOOM-3-BFG" fork of id Software's code by Robert Beckebans. There were improvements to Robert's Doom 3 BFG through January of this year but since then I hadn't heard any more from its developer or any other interesting open-source Doom 3 projects.
Fortunately, in looking at Beckebans' GitHub this weekend, RBDOOM-3-BFG is still being toyed with as a native Linux port of the updated Doom 3 title. The most recent commits to RBDOOM-3-BFG are less than one month old and among recent improvements have been support for the SDL 2.0 release, FreeBSD fixes, OpenAL sound fixes, and other fixes. Besides Robert Beckebans working on this code, there's also commits from a Daniel Gibson.
Those wanting to try out Doom 3 BFG on Linux can fetch the code from this GitHub repository, but you'll still need to own a copy of the Windows version of Doom 3 BFG in order to load the data files for the game.