There are at least two ways in which we can make this case.
First, we can argue that it constituted a moral turning point in the war from our point of view. Up until this time, we could say that we were just trying to support the non-communist government in the South. After we sanctioned the coup (even if we did not sanction the killing) we were no longer just supporting their government. We were, in a sense, dictating who should be leading that government. General Westmoreland, for example, believed that this meant that we were now irrevocably committed to running the war and trying to run the country.
Second, we can say that the coup marked the end of any real hope for a legitimate government in South Vietnam. After Diem’s death, the South fell apart. There was a rapid succession of different leaders and more coups. This made it much harder to hope to win the war because it made clear that the South’s government was being led by a succession of power-hungry and unscrupulous men.
Diem’s overthrow, then, can be seen as a turning point in the war because it made the war qualitatively harder to win and increased our moral involvement in the debacle.