I would argue that it did not, at least no more so than in any war.
The things that the US government did as matters of policy in the Vietnam War (as opposed to the individual actions of soldiers like those at My Lai) were not clear examples of war crimes. The US government chose to bomb North Vietnam, for example. This was no different than the strategic bombing of Germany or Japan in WWII. The US used Agent Orange to kill crops and jungle trees. Given that the US did not know at the time that Agent Orange was dangerous, this is not really the same as the use of chemical weapons.
I will not argue that what the US did in Vietnam was the best possible policy. But I will argue that it did not constitute deliberate crimes against humanity.