Why does it say "b'Yad Ami Yisrael"?
Rashi: They will be My messengers to take My vengeance. Malbim - it will be via Mashi'ach ben Yosef, like the Nevi'im said.
Radak #1: This shows that this Nevu'ah is for the future (i.e. it was not fulfilled yet).
Radak #2: Perhaps this was during Bayis Sheni. Yisrael overpowered them and destroyed them. We do not know this, for matters of Bayis Sheni were not written in Nevu'os.
Why does it say "k'Api vecha'Chamasi"?
Radak: Just like My anger against them was great, so will be My vengeance.
Malbim: They will do according to My anger, which is stored for them for the end of days.
What do we learn from "v'Yad'u Es Nikmasi..."?
Malbim (14, 17): They will recognize that it is My vengeance. Regarding Edom it does not say v'Yad'u Ki Ani Hashem, for they already recognized Him.