I'm not a flat Earther, but I work in a laser lab and I think that's not a good demonstration (the helicopter is fine though). If they go three miles out on the lake, then for the laser beam to shift up by 2 meters all it would take is a vertical misalignment of two hundreds of a degree. In terms of precision alignment this is actually not that much, you can do it with a normal kinematic mount without any differential adjusters. However, that's when talking about everything being rigidly mounted to an optical table that is floating on compressed air to damp out vibrations. They're using a laser mounted on what looks like camera tripods, and it's standing on a beach, that's not a stable surface.
Furthermore they don't give any explanation for what they use as a reference for their alignment. What I mean is, how are they sure that the beam is straight? They can't measure it by looking at the beam spot far away, because then they would be assuming the thing they want to measure. This is actually the key point of the whole experiment, and the fact that they don't address it means that the demonstration is pointless, and such "demonstrations" only give fuel to flat Earthers.
There are better ways of doing the experiment, for example setting up two lasers on either side of the lake, measuring the height (not precisely, but a few orders of magnitude more than the expected drop) of both of them, and then aligning them to each other such that they're parallel. Then the laser isn't parallel to the water any more, however you will still see the beam height change as you go across the lake. Specifically, it should change in a way that is symmetric around the half way point between both lasers. This symmetry directly proves the curvature, and eliminates the need for an ultra precise reference.
www.newsweek.com
