In this video you can see the strobes of an Approach Landing System. (Close the ad. so you can see them better, at the bottom of the frame.) The strobes are synchronised so that a light appears to speed toward the runway.
How fast is the apparent speed of the light?
It looks like the entire series is strobing front to back twice per second, so you’d just have to know the distance between the first & last light and do the math:
D × 2 × 3600 = feet per hour ÷ 5280 = MPH
D = distance between first & last light
I couldn’t get the video you linked to, to run, but I found this video on YouTube that describes the “International Standards and Recommended Practices for Aerodromes”.
I didn’t watch all of it, but it seemed to be pretty comprehensive and detailed in the layout and dimensions of the different lighting systems used, and it also confirmed Hail Ants description, that ‘the lights strobe front to back, twice per second’.
(1700 posts! And it only took me 14 years.):smack:
For the record, although it’s an optical illusion and there’s absolutely no actual motion whatsoever, if the first & last beacon are 500 feet apart then to the human eye the dots of light are moving at an apparent speed of over 600 MPH!
D should be easy to measure using Google Earth. The OP’s video specifies the airport and runway, and Google Earth includes a distance measurement tool. OP can visit the airport/runway, find the first and last lamps in the ALS, and size it up.
One important note:
There appears to be a brief pause between the time when the light closest to the runway extinguishes and the time when the light farthest from the runway illuminates again. IOW, the cycle time may be a half-second, but the actual transit time is slightly less, so the speed is a bit higher than your equation predicts.
That’s why I said ‘apparent motion’. 
600 mph looks about right, but I haven’t had time to do the math.
I think they actually appear to be moving more than twice that fast. On a MALSR, which is the approach lighting system in the video, the RAIL (aka the rabbit) consists of five strobes each placed 200 feet apart, for a total distance of 1000 feet, covered twice per second. As Machine Elf noted, there is a slight delay between the end of the sequence and the beginning of the next, so you can’t just say it’s 2000fps; it’s even faster than that. However, as you can see here it doesn’t look abnormal at all from the cockpit.