Elamites are also mentioned in Act 2.9.
That's the guy, Kudur-Lagamal. Like later Middle Eastern empires, he relied on manpower from tributary cities to keep the rest in line. The exact number of fighters Abraham had with him is in the OT acc't, and it's pretty small, suggesting that the Elamite king was A) killed in the battle, B) had something else to deal with and marched out with the bulk of his forces, leaving a skeleton crew to herd the booty caravan back to Elam, and/or C) had a rebellion break out among one or more of his allies, or even a coup back in Elam itself.