I see the wisdom of this law being passed in Taiwan. Recently I came down with a case of bronchitis, and wherever I went in downtown Nanjing, there was someone lighting up a cigarette... in the restaurant I went to, in the department store I visited, even in the washroom. It contributed to my illness, so I ended up just staying home when I wasn't at school. (Even in the hallways at school, people are allowed to smoke on their breaks.)
It really depends on the culture at large as to whether or not private businesses will turn a blind eye to smokers, or be more activist about it. In China, it feels like no one cares about indoor smoking. Everywhere you go is second hand smoke, and frankly I am tired of it.
I understand the principle of letting private businesses allow smoking, and therefore non-smokers should exercise the choice to not go there... but in a place like China, every single establishment is going to have someone lighting up. So if I want to avoid making my bronchitis worse, I just have to stay home, because as a non-smoker I have no choices left.
I think the individualistic approach works in the West because the culture at large is divided over the issue of smoking. You will always find establishments that forbid smoking, so non-smokers have choices. But in Asia where population density is higher, there is no escape from smokers, and smoking is very much related to status so everyone flaunts it, legislation is needed.