I think the answer is as follows. The Megillah wasn’t written in this manner by accident. On the contrary, it was written in this fashion precisely because the authors wanted to communicate the message that there was a cause and effect sequence. While an ordinary person might not see the Guiding Hand in these events, Mordechai and Esther were able to connect the dots. To them, it was eminently clear (at least in retrospect) that the feast was only meant to get rid of Vashti and clear the way for Esther. Mordechai HaTzaddik was able to recognize that Hashem didn’t allow Haman to rise to power until Achashverosh was first indebted in some way to him. That is why the word achar is used – to show how the sickness (Haman’s elevation) was immediately preceded by the cure (Mordechai saving the king’s life). The Megillah was written to allow one to see that many disparate events spanning a decade are interconnected and part of a plan being orchestrated by the ultimate Master.
This idea is the higher reality revealed on Purim. There were no open miracles on Purim, true. But when Mordechai and Esther managed to connect the dots and recognize Hashem’s guiding Hand in daily events they seized the moment and wrote Megillas Esther – a concrete description of Hashem’s complete involvement in our lives.
So what does this have to do with Amalek? The nation of Amalek embodies the antithesis of this worldview. While we struggle to see hashgacha (Divine Providence) in every step of life, the Amalekite philosophy is that everything is random. The Chumash and the Megillah refer to Amalek with the word “kor” which means “happenstance.” Amalek believes there is no Guiding Force; that what happens in this world is a chance occurrence, a coincidence, or a matter of luck. This we cannot tolerate. The Torah doesn’t demand that everyone be Jewish. All people, Jews and gentiles, can form a relationship with the Almighty. That is why the world was created. But if a nation denies or is unwilling to fulfill the sole purpose of this planet’s Creation, it has no place on it.
This is why the mazal of Adar is Fish. Fish are unique creatures in that they have no eyelids. Their eyes are always open. This alludes to the fact that the Guardian of Israel neither sleeps nor slumbers. His eyes are always open, watching us and guiding our every step. Now we can understand why this chag is called Purim, lots. Although the lottery that Haman drew may seem to be nothing more than a minor detail, we are supposed to realize that the entire story of Purim is that of the eternal struggle of the warring philosophies of the Powerball versus Pisces. Are all things random or part of a master plan?
May we merit to open our eyes and see G-d’s guiding Hand in every step of our lives.