Unfortunately there is a big difference between technically working, and performing adequately.
If you can run a first person shooter, without crashing, but attempting to aim at something means the game hangs for thirty seconds and then your view jumps to a position before hanging for another thirty seconds, it doesn't actually work.
The minimum should be what is required to have the game perform it's basic functionality at base settings, low resolution, none of the bells and whistles, not simply what is required for it to not crash. It's more subjective, but it's relevant to the question of whether or not you can actually use a product, whether it crashes or not is a non-subjective measurement, but doesn't tell you whether you can use it.
Recommended, naturally, is what it takes for the game to look great and run well.