You are more than half-way there. The words you left untranslated are perhaps less than 12 now.
When Themistocles was marching with the Athenians against the barbarians, he witnessed a cockfight.
or, adapting it to what you had so far: When Themistocles against the foreigners was leading out the Athenians, cocks he saw fighting.
When he saw that (note, it's a temporal participle), he halted the men and said to them: "these here (i.e. the cocks) aren't suffering for some homeland or some gods, nor for fame or freedom or their children, but only in order each one (ἔκαστος) not to lose, and not to give way (εἶξαι, from the verb εἴκω) one to the other"
The last sentence you can translate on your own. It's easier than the parts you already translated. Give it a go.