For those who can't see the video, Kurtz says:

"I remember when I was with Special Forces. Seems a thousand centuries ago. We went into a camp to inoculate the children. We left the camp after we had inoculated the children for polio, and this old
man came running after us and he was crying. He couldn't see. We went
back there and they had come and hacked off every inoculated arm. There they were in a pile...A pile of little arms. And I remember - I - I - I cried. I wept like some grandmother. I wanted to tear my teeth out. I didn't know what I wanted to do. ... And then I realized - like I was shot. Like I was shot with a diamond - a diamond bullet right through my forehead.

"And I thought: My God! The genius of that! The genius. The will to do that. Perfect, genuine, complete, crystalline, pure....And then I realized they were stronger than we. Because...[t]hese were not monsters. These were men, trained cadres,these men who fought with their hearts, who had families, who had children, who were filled with love. But they had the strength...the strength...to do that! If I had ten divisions of those men our troubles here would be over very quickly.

"You have to have men who are moral, and at the same time who are able to utilize their primordial instincts to kill without feeling, without passion, without judgement - without judgement. Because it's judgement that defeats us."

The "horror" is no less than sixfold:

The atrocity itself.

Kurtz's realization that the perpetrators were (once, anyway) ordinary men.

His conclusion that their kind of "strength" is necessary to win the war.

Kurtz's implicit decision to adopt similar tactics. (That's why Willard is there to kill him.)

The earlier information that Kurtz has a PhD and was once a model officer.

The fact that exposure to atrocity has stripped him of his own humanity.

(More "horror" than Conrad's Kurtz succumbs to?)