Despite the 2 GB VRAM and 8 System RAM requirement, I got BF1 multiplayer running on my wife's i3-2120 / 6GB / Radeon 7750 1GB machine, and I didn't even have to mess with anything like a CFG file to do it.
For the Mount Grappa map at 1080p, medium settings is doable for the 'ol cut down Cape Verde GPU (runs ~30 FPS) until it hit the obvious memory limit and has to swap in/out textures & data. Of course the system memory was completely saturated too, likely contributing to the problem, but not as much as the VRAM was.
1080p, Low settings is definitely the only real way to go if you're stuck with such a paltry graphics card in terms of VRAM, and setting resolution to 720p freed up even more VRAM, got it down to ~900 MB in use.
The Empire's Edge map was much more unforgiving, as 720p and all lowest settings still created a stutter nightmare at times. However, from a purely objective point of view, the Radeon 7750 is still quite a performer when it has enough VRAM. I really have to give props to DICE for optimizing the hell out of the game.