I chatted with ESRI on this and got an answer! In general, when ESRI in the article refers to post-processing, they are referring to traditional geoprocessing.
Field Maps only stores shapefiles, geodatabases, feature services, etc - but not the information that would be usually needed to post-process GPS data after collection in the field. So unfortunately - GPS data gathered with Field Maps can't be post-processed into some else (like GPS Pathfinder, for example).