Huh, and here I thought the Hollow Earth theory had been discredited, but I guess I might believe Raytheon and its lasers. Cyrus Teed would be so pleased.
As an example, if you're at the North Pole and the South Pole base fires a ballistic missile at you, you can't aim a laser at it, as it would diametrically intersect the Earth.
Instead, you have to wait until the missile passes your horizon. The point at which it does this depends on its altitude. Hypersonic vehicles attempt to make interception harder by reentering the atmosphere from space earlier than a traditional ICBM, and travelling at a lower altitude in their final phase.
No, on a sphere a laser shot towards the horizon will not hit the Earth's "curves."
Shooting towards the horizon is by definition shooting tangentially to the surface you are on. The horizon is the point where the sky meets the land or sea. If you make a straight line from your laser to the horizon, it will continue out into space.
Your explanation of what they meant makes sense: a laser shot towards a distant target, not towards the horizon. But that's not what they said. And, obviously, I did not actually think the fault was the engineers' but the journalist's explanation.
It's certainly an issue when that "other" side is the outside.