The cstore_fdw extension uses the Optimized Row Columnar (ORC) format, which seems to be PAX in your nomenclature. The improvements he accomplished seems to be related just to the first "fact" that you listed, which applies to all column stores.
Not all columnar formats have great CPU streaming performance and even then it is data type dependent. Many columnar formats have significantly worse streaming performance than vector formats because only the latter is primarily optimized for it and column stores will trade that for other things (like format compressibility). And for data types that have no mathematical order of any kind e.g. interval data types, columnar formats effectively degenerate into very inefficient vector formats. It is still an open academic discussion.