Phylogenetic methods have been used to infer the relationships of things other than genes, organisms or species, or indeed, anything biological. Language, culture, political systems, religions, stories (including most recently, Red Riding Hood), and so on.
I train in martial arts, and I think it would be really interesting to do a phylogeny of the different martial arts. There are many folk histories about how the different fighting traditions have evolved, and some of these have been passed along as fact, although its pretty obvious in many instances that they cannot be true. There has also been quite a bit of politics involved in taking ownership of different forms because of the ebb and flow of national and cultural borders.
I’m pretty certain that there has been no real scientific study of the relationships between these arts. It would not be too hard to do, I think. Of course, one would have to figure out ways to account for “borrowing”, but the language phylogeneticists have been doing this.