Hmm, the cities files are just a list of gazetteer entries. Individual places. Large population centers. A filtered subset of the full geonames gazetteer table.
Don't think the table as any explicit cross-references. Any real admin hierarchy is not in the cities file alone, that sort of data comes from other files.
I don't know what the error you saw are, but perhaps it expecting a certain number of cities in particular countries. You removed too many?
Or maybe it expecting at least one PPLA per country, and you happened to remove them? (there may be seats with less than 50k pop)
If filtering by population, may want to also make sure NOT filtering PPLA*/PPLC records? (in the featurecode column)