We are commanded to remember and never to forget – not Amalek per se, but what Amalek did to us on our way out of Egypt.
This allows us to include in the "definition" of Amalek, those who are Amalek-like; those who behave like Amalek, and like his famous descendant, Haman.
We should also keep in mind who Amalek's grandfather was and who filled the original Amalek with hatred for the descendants of Yaakov. It was Yaakov Avinu's twin, Eisav.
As to the mitzva of TIMCHEH, eradicate the memory of Amalek, there are issues of to whom this mitzva applies: the king of Israel, the people as a whole (its Sanhedrin), and/or the individual Jew. There is also the significant issue of our inability to identify an actual descendant of Amalek in our time.
In addition, there is the opinion of the Brisker Rav that no one can fulfill this mitzva until instructed so by a true Navi. But if we focus on the mitzvot of Zachor and Lo Tishkach – Remember and Do not forget, we will still be able to define Amalek, and more significantly, to define what we are supposed to remember, what we are supposed to never forget, and even what we are supposed to try to rid the world of.
Let's take Hassan Nasrallah as an example. Is he a descendant of Amalek? We don't know. End of story? Not quite. Do we include him in our vigilance against forgetting what Amalek did (and what they wanted to do!)? Definitely. Do we include him when we are in the process of remem- bering? Definitely.
The litmus test is not his lineage, it is his remarkable resemblance to Amalek, his grand- father and his descendants. When we hear the Hizbola leaders talk about the destruction of Israel, we hear Eisav talking. We hear Amalek attacking. We hear Haman desiring to destroy every man, woman, and child – the nation of Mordechai.
We hear Hitler ranting and raving, and, sadly, doing, as well. And even if we can't wipe him – and others like him – out, we certainly can and must work towards neutralizing him, fighting anti-Semitism and Anti-Israel attitude and behavior, with renewed commitment. ZACHOR is not paying lip-service to an idea – it is remembering and never forgetting so that we will prevail over the Amaleks in the world.
The battle against Amalek is MIDOR DOR, from generation to generation – and G-d fights along side of us. There's another aspect of ZACHOR – to remember that it is our lack of total commitment to Torah and mitzvot that makes us vulnerable to the Amaleks of the world. Improving ourselves – as individuals and as Klal Yisrael is our best weapon against Amalek. May we remember, never forget, and succeed against Amalek.