The story is The ReplicatorsThe Replicators by A. E. Van Vogt.
The opening paragraph in which the protagonist Matlin first kills the alien is:
Standing there, after killing the monster, Matlin began to get mad. In its death throes, the twelve-foot creature had done a violent muscular convulsion and somersaulted over into the dump section of Matlin’s truck. There it lay now, with its elephantine head and quarter-length trunk twisted to one side, and a huge arm and hand flung up and visible over the rear end. What must have been tons of shiny, black body was squashed limply down into the bottom of the cavernous metal carrier . . . creating a problem. That was all it was to Matlin: a problem.
The reference to the King Marine syndrome comes when the army start shelling the alien ship to deliberately induce King Marine Syndrome in Matlin (this is General Day speaking):
"A king Marine, Mr. Graham, can direct a war, take command of a city, or negotiate with a foreign power like a government. Marines who get to be generals are considered sub-level versions of this species. All Marines understand this perfectly. It will not occur to Matlin to consult me, or you, or the U.S. Government. He’ll size up the situation, make a decision, and I shall back him up.”
He turned to the major, commanded, “All right, start firing!”
At the end Matlin doesn't exactly surrender, but he throws his gun down as a gesture of friendship:
As he saw the creature, Matlin used his gun for the purpose that he had brought it. Deliberately, he tossed it down. It struck the metal floor with a clatter. The echoes of the sound faded — and there was silence. Alien and human stood there staring.
