By listening or reading the megillah is the mitzvah of zecher amalek being fulfilled?
The Maharam Schick Mitzvah 605 says that the mitzvah is to specifically read from a Sefer Torah in public with a minyan. He brings others who say reading the pesukim alone may work as well, but none that suggest the Megilla is an alternative.
As was pointed out in the comments, there are those who hold the whole mitzvah can be accomplished just by remembering it in your heart. However, the Minchas Chinuch in Mitzvah 603 states that even according to those opinions, there is a rabbinical requirement to read from a Sefer Torah:
כל פנים זה ודאי ברור דהמצוה ביחיד ג"כ מקיים רק פ' זכור בעשרה ובס"ת הוא מדרבנן אבל מן התורה די שיזכור בפה כל יחיד וז"פ.
More specifically to the question asked, the MB 685:16 brings a Magen Avraham that talks about someone who can only get a minyan for either zachor or Megilla, and says that he can be yotze the mitzvah of Amalek with the Torah reading of Purim morning. (The MB disagrees and says zachor is more important). From the fact that he didn’t mention using the Megilla, and the fact that the MB argues with him because the Purim torah portion doesn’t mention the mitzvah, it would seem that the Megilla is not counted according to all opinions.
Seemingly here https://www.sefaria.org/Peninei_Halakhah%2C_Zemanim.14.6.6?lang=en&with=all&lang2=en there is an opinion (although only one) that reading the megillah does qualify for the mitzvah of zecher amalek