In the first one - you haven't quite parsed it correctly. It is the compound noun 'sociopolitical change in cities' that was in mind - and if you wanted to simplify that - it would be to 'change' rather than 'cities'. Change, of a sociopolitical nature, that occurs in cities. 'in mind' just means 'they were thinking of', or in this case, where it probably isn't a person thinking, it is perhaps 'as an ulterior motive'.
'playing out' is more-or-less 'occurring' - but it has a definite nuance of being very convoluted. I suspect it comes from the idea of a play, or drama - where the complex plot 'plays out' over the course of the production.