

Just because it’s not mechanically automatic, does not mean it’s not a launch on warning system.
The key phrase there is “it does not rely on a launch-under-attack policy to ensure credible defense”
If the US detects a ICBM launch, it will launch a response. It does not matter if the thing that presses the button is a person or an automated program.
Launch on warning just means a country won’t physically absorb a nuclear strike before launching, but will launch if an enemy launch is detected. It has nothing to do with automatic launch systems.
Maybe you should read the entire story, it’s not that long.