In 1981, Hugh Carey was governor of New York.
According to Wikipedia:
He is also remembered for preventing conservative legislators from reinstating the death penalty
So the subject of the death penalty would certainly have been on his mind.
My understanding of the responsum is Rav Moshe is not weighing in pro or con per se regarding what the State of New York's stance should be; he is simply explaining and defending the theoretical use of the death penalty in the Torah. I don't know who translated the letter to English, whether Governor Carey read it, or if it affected his decision process in any way. (Rabbi Aaron Soloveichik, in contrast, was quite vociferously opposed to any modern-day death penalty.)
There are several indicators that the letter was addressed to the governor:
- The language Sar HaMedina. See for instance the prayer for the US found in the Tikun Meir siddur, which blesses "president so-and-so", "vice-president so-and-so", the country's legislators and justices; and then sar hamedina and his/her second-in-command; followed finally by "the head of this city" (rosh ha'ir hazot). By context, then, sar hamedina v'mishnehu must refer to the governor of the state (and his/her lieutenant governor).
- I am not aware of any other executive who would have been reconsidering the death penalty in 1981. I don't believe the mayor of NYC, nor the president of the US, was doing so; and the language sounds as it it's addressed to an executive, not a legislator or justice.
- The letter concludes with blessings to sar hamedina for his continued successful leadership "within this wonderful country of the United States of America", implying that sar hamedina is not himself the president of the US.