I thought that was a pretty neat shot... It doesn't say much to me about the overall shape of the earth..
If there are sufficient landmarks or other geographical features, and a reasonably cloudless sky, then, as with the Red Bull Space Jump footage, it can be determined whether or not the landmarks are within the viewing scope of a spherical cap, based on the orbital height or altitude of the craft.
What I've seen of the Inspiration footage thus far seems plagued by cloud, though...
Couldn't the same test be done from a Cessna 150 or the top of the Empire State building? The math would work just as well, and landmarks would be easier to see.
In theory, yes, but the visibility from aircraft tends to be limited by haze - usually particulate matter in the lower atmosphere - and not curvature. On a clear day, you might have, say, 20km visibility (met forecasts usually stop discriminating at 10km) at the kind of altitude you might reach in a light aircraft. But if you climb above the haze layer, or indeed the troposphere, such as in the red bull situation, or a rocket, you will be able to see a lot further, as the haze layer is less thick than, say 20km, meaning you can always see through it.