I don't doubt the quad launch, just that animation of it.
If the animal can just get itself gliding, I think it is possible to continue generating lift even while raising its wings into position for a downstroke - what it needs to do is maintain a positive angle of attack while doing so. At least when they are not hovering, birds continue to generate lift on the upstroke.
A headwind would make it easier, and perhaps that or a downslope might have been necessary.
Yes, that's a jump. This is a very light animal relative to its wing strength, it should be able to jump very high.
By the article, those animals should be stronger (relatively to their weight) than birds, only comparable to bats, and most people simply don't believe the kind of maneuvers bats can do.
I trust the simulations mentioned in the article take this into account, but the grandparent is right that this is not it all obvious from the video. In fact the video shows very leven flight motion while the wings are brought up, which absolutely would not be the case.
The key bit is right at the end, showing launch in real time. There is no descent for lack of lift because there is no time for it to happen in. While the animal is still rising from the jump, the wings swing out and take up the load, in a fractional second.
It would be terrifying to have it happen toward you, even as it swept over.