The Parthian empire can be considered to be persian for multiple reasons. First the tribes that you named are of iranian cultural background, even if they are (semi-?)nomads. In addition one they conquered the iranian plateau from the Seleucids in the great offensive of 138BC they simply controlled more or less what we call Iran, even if Fars, the heart of ancient Persia (the region around Persepolis) was still held by vassal kings called the Frataraka(s). Finally the expression of their royal power reused some elements of the persian empire such as the upright tiara (not the jewel of course). This element is easily visible if you compare the coins of parthian kings. The first would have hellenistic royal headband but later they would combine the two or carry the a tiara reminiscent of the Achaemenid. Last but not least they laid claims to the territories of the Achaemenid persian and Alexander's empires. In a few lines of Tacitus (6,31) a Parthian king threatens roman ambassadors threathening the Romans on the subject. They also built a palace specifically on an old palatial complex of Artaxerxes II and reused the title of "great king", even if some seleucids did it earlier like Antiochus III the great (followed by their neighbours in Parthia, Bactria and Armenia).