Being from Brazil, I was reading that list and also remembered that recent finding, and I started wondering whether there could be any historical process by which Latin America acquired such high rates of criminal violence.
I know that this question could be asked to social studies (e.g., a matter of classes or institutions) or to economics (e.g., it's all about wealth inequality), but I was rather interested on the historic perspective of this subject.
It would be difficult to trace a clear "causal" reason for violent cities, but some factors that one could consider:
a) the extremely violent nature of colonization in Latin America, which involved the death of millions of indigenous Americans through armed conflict and disease; this was often excused under rhetoric about "spreading civilization" and based on racist views towards these sections of the population which still persist, to some extent, today.
b) the violent nature of slavery of both indigenous peoples and Africans brought to the New World to work on plantations...black slavery continued in places like Brazil until the late 19th century and included brutal punishments under the ideology of maintaing order/production.
c) the building up of military and police strength under dictatorships in the region in the 1960s and 1970s, often with financial support and at times even training and military resources from the United States
d) the long and deep history of inequality in the region