I use a dinosaur with win xp/Sp3, 1gb ram and 256vram (the bottom line of requirements).
And i play with all mid range settings, AA enabled and insane 1920* 1180, avoid the cloth map (it's plain ugly!) and
never use auto resolve. The game runs smooth and fine for around the first 50-75 turns, than starts lagging and...
Get a swap file around 1,5gb around 75-100 turns, save&exit, start&load allows me to play another 20 turns till OoM kills my machine.
This looks for me not like vram issue - thats a giant cpu memory leak.
The gama data load itself seems to get too huge....