For anyone with a biology background, having traits shared through common inheritance should ring a bell. Evolutionary biologists have long been able to build family trees of related species, called phylogenetic trees. By figuring out what species have the most traits in common and grouping them together, it's possible to identify when certain features have evolved in the past. In recent years, the increase in computing power and DNA sequences to align has led to some very sophisticated phylogenetic software, which can analyze every possible tree and perform a Bayesian statistical analysis to figure out which trees are most likely to represent reality.
By treating language features like subject-verb order as a trait, the authors were able to perform this sort of analysis on four different language families: 79 Indo-European languages, 130 Austronesian languages, 66 Bantu languages, and 26 Uto-Aztecan languages. Although we don't have a complete roster of the languages in those families, they include over 2,400 languages that have been evolving for a minimum of 4,000 years.