We normally “spiritualize” this, with the “enemies” referring to the demons who assault us daily in our thoughts. The references to Amalek in the vigil for this feast seem to refer to the demons."
We normally sing it in the original Greek with the original word Βαρβαρων "Varvaron" which you are translating as "adversaries" meaning Barbarians. The history of this chant is to an extent political and from a time when the Cross was used as a defense against the attacks of barbarian hordes
Here are the words to the Troparion:
"Σώσον Κύριε τόν λαόν σου καί ευλόγησον τήν κληρονομίαν σου, νίκας τοίς Βασιλεύσι κατά βαρβάρων δωρούμενος καί τό σόν φυλάττων διά τού Σταυρού σου πολίτευμα."
And here is a link to the chant:
http://www.youtube.com/watch?v=5Z8qfKoUBKY
As we all know, Kolo, even today—both here in the US and in the Serbian homeland and elsewhere—we are still assaulted by barbarian hordes.
However, we all have our spiritual warfare, too.