In reality though, you did not achieve your military aims and therefore lost.

Our goal was to force a North Vietnamese surrender. We accomplished that.

War isn't about death tolls, by that measurement you could argue that the Germans won the war in the East in WW2, when the reality says otherwise.

And by the logic you are using, the Soviets lost WW2 because eventually East Germany was reabsorbed into Germany and became unified.

The US only won the war, if you change the parameters of warfare to inflicting damage, as opposed to achieving aims.

Johnson achieved his aim, which was to force the NVA to sue for peace. Nixon also achieved his aim, which was to remove American troops from Vietnam regardless of the consequences. Nixon didn't achieve Johnson's aims, but that is the nature of American politics. There is no one singular mind guiding American policy.

To say that we didn't win the war is to say that we lost the war, but we clearly did not lose the war. When American left Vietnam, was the South Vietnamese government still standing? Yes. Did the North Vietnamese force an American withdrawal? No. Did we withdraw by our own choice? Yes. So how did we lose? Who did we lose to?

The South Vietnamese lost. We didn't lose, we stopped fighting and went home. We changed strategies, but changing strategies is not even close to the same thing as losing. And since we were successful in pursuing our new strategy, we won.