Jamieson, Fausset and Brown on Isaiah 21:2

2. dealeth treacherously--referring to the military stratagem employed by Cyrus in taking Babylon. It may be translated, "is repaid with treachery"; then the subject of the verb is Babylon. She is repaid in her own coin; Is 33:1; Ha 2:8, favor this.

Go up--Isaiah abruptly recites the order which he hears God giving to the Persians, the instruments of His vengeance (Is 13:3, 17).

Elam--a province of Persia, the original place of their settlement (Ge 10:22), east of the Euphrates. The name "Persia" was not in use until the captivity; it means a "horseman"; Cyrus first trained the Persians in horsemanship. It is a mark of authenticity that the name is not found before Daniel and Ezekiel [Bochart].

thereof--the "sighing" caused by Babylon (Is 14:7, 8).