A quadrotor (or 8-rotor here) drone depends on rapidly throttling the propeller speed on each arm up and down, something that you can't do with a mechanical transmission without adding a lot of weight. You can do a gas/electric hybrid, but again, weight.
I kind of also wonder why not a more traditional articulated rotor helicopter design. The point of the quadrotors is they're cheap and simple, despite being much less efficient. Surely the capital investment in a full fleet of these things would favor a true helicopter rotor.
Noise would be an issue with gas powered drones.
Cars aren't that noisy, and drones are going to be high up in any case.
Cars don't have eight rotor blades slapping the air, and we've gotten pretty good at enclosing all the loud bits (on expensive cars). Noise would certainly be a problem for gas-powered drones.
And gas powered cars are a lot louder than electric cars.
To minimize noise and visual pollution, it would be better for these drones to fly low, along existing roads to take advantage of existing noise abatement measures (e.g. noise barriers walls, berms, roadside vegetation, etc.)