He clearly means
this one.
I don't know, from this period I only read texts that dealt with the present. I think people in the West tended to care about the events around Cicero, Caesar, Hannibal and other classical Rome stuff which is now famous in the West, because the texts that were used to teach Latin either come from that period of time or they talk about these events. For example take the Catilinian conspiracy, which would be a completely random event, that no one would probably remember if it happened like in the 3rd century, but Sallust, one of the greatest classics wrote a book about it and Cicero, the number one classic, wrote multiple speeches about it and kept ridiculously boasting about how he stopped it and saved the polity until the end of his life, so it is quite well known and it even became inspiration for the awful Megalopolis film today. But Byzantines wrote in Greek so they had other authors to study as examples of excellent style and those mainly cared about stuff happening in classical Greece, so for them the events that we consider as super important would not matter as much (because honestly many of them were not very important) and they would probably remember other people more, Constantine for sure, and maybe Justinian, Heraclius and so on.