Part of my argument in the above post was that, in terms of qualitative method, the major advance complexity science makes is the qualitative study of numerical data. To demonstrate this point, click on the following link to the Santa Fe Institute (the leading world institute for the study of complexity) and, in the search box, type in "qualitative method." You will get roughly 700 hits. Almost all of them contain the terms qualitative and numerical.
You will find, however, almost no mention of qualitative method, as it is understood in the social science sense of the term. This is not to say there is no such work being done. But, it by no means has a dominant voice.