Hellenistic philosophy came after those guys; IIRC the biggest schools were the stoics and epicureans, with the peripatetics (following Aristotle) in third place. Plato got more influential in the later Roman empire, after Hellenistic times. So your comment kind of supports the grandparent's point (your "little bit of pre-Socratics" means the "early Greek" GP mentioned).

A cute bit for us computer nerds: Chrysippus pretty much invented boolean logic (in the Hellenistic period) and was considered the Father of Logic in antiquity. My intro philosophy course with a heavy emphasis on formal logic never mentioned any of this.