I see no problem playing D3 BFG via wine 1.5.15+, but of course you can use steam (-no-dwrite) just to download everything only as soon as somebody manages to port it to Linux. The video playback must be changed as well but should not be that problematic as libav/ffmpeg can play the videos directly, most likely you just have to force the 16:9 aspect.
It seems someone has already ported Doom3 BFG to Linux or atleast it compiles and runs. Sound doesn't seem to work but otherwise it runs just fine.
That's really cool, just tried it but there have been some mouse issues. caedes told me that there is another repo with a branch that fixes those:
Basically it works but no videos/sound yet. I would not use fullscreen because alt-enter/alt-tab does not work yet. So start it like:
I hope to hear something soon and see the videos, then it would be perfect.
./RBDoom3 +set r_fullscreen 0