Leaf shutters solved rolling shutter for still images a long time ago, but they cannot be used for video.

Film video cameras use rotary shutters while digital video cameras do not use any mechanical shutter at all. The rolling shutter effect in digital video is a consequence of not being able to do a readout of charge on all photosites at the same time, or more technically, fast enough that it doesn't matter.

"Global shutter" in this sense is not a mechanical shutter. It's technology on the image sensor. Maybe a better term is global electronic shutter. Unless it's a fundamentally different tech, this would work the same as any image sensor, just faster. A good image sensor these days will complete a readout in under 20ms, so if they are calling this much better than what they already sell to the point they brand it as a 'global shutter', I would guess it's in the range of 1ms or so.