The authors identify several ways that corruption might influence the risk of accidents, such as by undermining infrastructure development, limiting opportunities for economic advancement, or discouraging legal enforcement. It is the last that O’Malley identifies. There are countries where police are powerless or unwilling to enforce the laws, and as a result drivers tend to ignore them.
Another 2010 study found similar correlations between governance and traffic deaths, and then went on to look at cultural factors as well (paywall). Certain cultural values, such as intellectual autonomy, were seen to reduce traffic fatalities. Others, such as having a hierarchical social structure, made them more common. Good governance was found to be an effective moderator of some of those values that would otherwise increase fatalities. In countries with ineffective governments, negative cultural effects are likely to be more pronounced.
None of these correlations can fully explain the mechanism by which corruption influences traffic fatalities. However, numerous different analyses, using different datasets, support the idea that they are somehow connected.