That was a back-room diplomatic deal -- it was still officially, publicly, an unconditional surrender. By not hanging the emperor, Truman allowed the Japanese to save a little face, and gained a pliant figurehead who would be helpful in rebuilding and reforming Japan.
The term unconditional surrender was never used in the agreement. I doubt that he cared at all about the Japanese saving face. Truman feared the losses from a ground invasion. After all, he knew full well that we had a limited A bomb stockpile. Regardless of any later spin (and that's all it was), his New Deal advisors were quite upset at what they perceived a cave.
We have the results now to show the success of the Japan strategy in that situation.