Given the additional information that you have given under your question, it is clear that Zippo should pursue a multi-domestic strategy. The reason for this is that the different markets appear to have very different needs.
A multi-domestic marketing strategy should be pursued when there are differences in the sort of strategies that will work in each market. In this case, we can see that Zippo lighters need to be marketed much differently in China (as a luxury good) than in America (emphasizing utility with respect to security procedures). This shows that lighters are things that should be marketed differently in different countries. Therefore, a multi-domestic approach would be best.