From the beginning of the principate Augustus favoured his blood relatives for the succession, only turning to Tiberius after his grandsons had died. Even then Tiberius was adopted as Augustus' son. When Augustus died, the new Emperor thought it best to have Postumus Agrippa assassinated, although Agrippa (who'd spent the past few years in exile on a rock in the middle of the sea) had no experience or qualifications for the throne other than being related to Augustus. Caligula and Claudius were both popular (although in Caligula's case this ended up waning) because of their familial relationship to Germanicus. When Claudius made Nero his heir instead of Britannicus this was widely attributed to the machinations of his new wife, the implication being that Claudius would naturally be expected to choose his own son as successor. Again, when Nero came to the throne, almost the first thing he did was murder Britannicus, who had the potential to be a rival due to his relationship to the previous Emperor. And so on. Even during the Republican period a politician's clients would pass to his heir on his death, and coming from an established political dynasty was a big boost to somebody's prestige and chances of political success. The Empire continued this. So, as I said, not as dynastic as Mediaeval Europe, but certainly more dynastic than modern politics.