No, your computer will not take damage from it unless it overheats.

The game itself might not run very well though, and you might get some crashes if memory runs out or similar.

The most noticable effect of lower CPU and Ram is very slow performance. As for video card, the lower you have under the minimum required, the more ugly and unrealistic the graphics will look, and it will also put more load on your CPU. You're far more likely to run a game successfully if you have a slower CPU, than if you had a slower video card. Think of it as a guideline for having the best experience playing it. If you go below, you're chancing some really choppy gameplay, and not being able to see it's graphics in an acceptable quality.