Tesla did not invent efficient power over air.
If anything, Tesla might have invented a reasonably efficient gas discharge tube that made him think he was transmitting huge amounts of energy through air. Carbon filament lights back then were probably less than 1% efficient. A 10% efficient glow tube right next to a Tesla coil might have appeared to be a clever invention. You can read the details of his plans and it was definitely crazy nonsense.
I lived a mile from an AM radio station at one point. The energy transfer is anything but efficient, but it does end up where it's unwanted. There was 1V @ 1MHz on practical everything. You could get free power if dimly glowing LEDs counted.
Back on topic, DARPA clearly made this to access funding that's not available for weapons. The power density of laser light is key for weaponizing it. Stating a goal of sending high power through a fine cable is clever.