It is very much part of a sort of Lost Cause myth of the Vietnam War that was very propagated after the war. The idea that "the United States and South Vietnam were "winning the war decisively by every conceivable measure" in "late 1972."' is evidently false. Of course, North Vietnam did suffer a setback in the Easter Offensive of that very year but it did not break their back and only highlighted the fact that the PAVN needed more preparation and training for a final conventional offensive.

The United States failed in the Vietnam War for a long list of reasons, one of the most important in my opinion is the lack of adaptation to the nature of counterinsurgency which the conflict demanded. I've written a large post on this matter right here.

So while there is no truth to the idea that the US and South Vietnamese were winning in any form, the latter part involving the promises, Nixon's resignation and the 'testing' of Gerald Ford isn't entirely false. Richard Nixon most certainly did promise the South Vietnamese military hardware and actual military help (presumably through air support, which had proven to work very well in 1972). With the Watergate Scandal and Nixon's resignation, that promise fell away. It isn't a lie to say that since the US was unable (and unwilling) to provide the South Vietnamese with military supplies, the North was able to gain a considerable advantage which led to final victory. However, it wasn't the only reason for which I can only refer to this post for elaboration.

I guess before anyone can answer your question it's necessary to define exactly what is meant by "winning" the Vietnam war. Was the central policy goal of the US in the Vietnam conflict the imposition of a US puppet in South Vietnam, with a permanent US presence? If so, then it is clearly the case that the American government lacked the political will to maintain and fund a long term American presence in South Vietnam, in the same mould of the residual force maintained in Korea. The decision not to this rout of a large residual American presence was made early in Nixon's administration, where instead the logic of Vietnamization, that is the goal of a South Vietnam capable of securing its own borders with only the assistance of American air power, technical support, and funding, was the focus of the conflict post-1969.

During this same period 1970-75, the US Congress passed a number of amendments to appropriations for the US war in South-East Asia. The first of these was the Cooper-Church amendment, which cut off all funding for US air and ground operations in Cambodia, as well as funding for any South Vietnamese operations outside the borders of South Vietnam. It is true that these amendments were all passed during a period of Democratic majorities in both Houses of Congress, however, they drew support and opposition from various elements within both parties.

What I believe the video is referring to, is that, while the Paris Accords ensured the withdrawal of all US forces from South Vietnam, the Nixon administration was confident that US airpower over North and South Vietnam would be suffice to stop any North Vietnamese violation of the Accords. However, the 1973 Case-Church amendment defunded all combat operations in South-East Asia, without prior congressional approval. The 1975 effort of the Ford administration to lobby for Congressional approval in response to the large scale Northern invasion of the South met with little success, making Nixon's promise to ensure the independence of South Vietnam through US air power worthless.