That's weird. I actually interpreted that as an argument in favour of a Flat Earth, because, once the sun sets (and the earth continues to spin at ~1000 mph) there is no way that getting up 1000 feet is going to enable you to see the sun rise again, even if you can do that in about 2 minutes (from the outside on the ground, to the elevators, then up the elevators)
But seeing how everything converges to the horizon on a flat earth, then getting up fast enough would enable one to see the sun "rise" again. Makes sense to me.
I think it's more like they watch the sun set inside the elevator or it has just set as they enter the elevator.
"The world's tallest building, Burj Khalifa, occupies third place in the list, with a maximum elevator speed of 36 km/h, or 600m/min. The engineers working on the design first thought about installing triple-decker elevators, which would have been the first in the world. The double-decker elevators that have instead been installed have a capacity of 12 to 14 persons per cabin."
http://www.constructionweekonline.com/article-20616-burj-khalifa-has-worlds-third-fastest-elevator/ For an observer standing on the ground with h = 1.70 metres (5 ft 7 in) (average eye-level height), the horizon is at a distance of 4.7 kilometres (2.9 mi).
For an observer standing on the ground with h = 2 metres (6 ft 7 in), the horizon is at a distance of 5 kilometres (3.1 mi).
For an observer standing on a hill or tower of 100 metres (330 ft) in height, the horizon is at a distance of 36 kilometres (22 mi).
For an observer standing at the top of the Burj Khalifa (828 metres (2,717 ft) in height), the horizon is at a distance of 103 kilometres (64 mi).
For an observer atop Mount Everest (8,848 metres (29,029 ft) in altitude), the horizon is at a distance of 336 kilometres (209 mi).
These are facts, not theory. But they happen to agree with RET. FET on the other hand would predict you should be able to see forever into the distance. The ad hoc argument that this ability is limited by the air leaves you unable to explain why you can see farther the higher you are above the earth.
With the FE sun at 2,000 miles altitude and say 8,000 miles away from you it'd be at an elevation of 14 degrees. So throw in another ad hoc supposition of bendy lightrays. The sun "sets" at a distance of just a couple of miles for someone standing at the beach. How bendy is that light?? Once the light bends to give the illusion of a sunset any viewing of the sun light from further away atop a tall building or mountain would require your bendy light to bend beyond horizontal and start curving up again. That would create the optical illusion of the sun at an angel below the horizon!
The elevator moves at 33ft/sec so would take 82 seconds to get to 2,717 ft high.
Rotation rate of 900mph (at Dubai) for 82 seconds = 20.5 miles.
The increase in horizon from the base to 2,717 ft up is 64 miles - 3 miles = 61 miles. You have 40 miles to spare.
Rotation rate is not an issue.