A historian's view: The timeline is screwed up.
For instance, the Battle of Jaxartes was three years after Alexandria by Egypt was founded. Further: the lyrics make no distinction between which Alexandria was founded. There were something like 18 Alexandrias founded, or renamed, by Alexander. Does it mean Alexandria on the Oxus? Alexandria Ariana? Alexanderia the Furthest? (which was less further than other Alexandrias)
And he swore to "free" Asia Minor? Worthington, I think I recall, argued for a possibility that maybe Philip II was seeking vengeance for the Persian Wars: conflicts in which Macedon generally sided with Persia. Implying they sought to expunge their own disgrace for being on the wrong side, politically, even if Persia does get a "technical victory" for removing Greece as a threat (assuming you disagree with ancient Greek sources which say Persia wanted purely conquest, which disagree with all other ancient sources which agree that Persia wanted to secure their flank by beating Greece down, which they did). Anyway, there's no real grounds for agreeing with Macedonian propaganda that Alexander sought "freedom" for Ionian Greeks. But a hell of a lot for generally agreeing with Greek propaganda that Alexander simply wanted to conquer. After all, Alexander would have achieved the former goal after one battle. And was offered it after Issus, and declined it "...if I were Parmenion".
Anyway.
Also, Darius fled after Arbela (Gaugamela), in verse 4, not in verse three. And fled isn't the right word. He sought to build a new army out of the majority of the empire that remained, but Bessus killed him. And Bessus is the one who fled, to solidify control over the eastern half of the empire. And the ensuing campaign is the rest of verse 3, as Alexander invaded Bactria and Sogdiana to secure recalcitrant Satrapys...and tangle with the Scythians to secure his northern flank in a similar way as the Persians probably invaded Greece to secure their western.
WHY DO YOU DO THIS TO ME, BRUCE DICKINSON?
Great song.