Judging from the placement of the two vehicles, it look as if the speed cant have been that much different between the two.
At night you can some times catch a plate if there are a little light ( and there seem to be ) and the difference in speed between the camera car and target car are less than the crawl speed of a grown man.
Anything higher than that and the chance of a plate capture dwindle very fast at night.
Other observations from the "picture " is the camera have probably dropped the exposure timing all the way down to 1:30 second, just "fast " enough to allow for 30 frames getting recorded every second.
And so the only other option to reign in lighting challenges is changing the ISO of the camera, and that are probably all the way up, also to accommodate a bright picture, so if the camera drop ISO to compensate for the bright store sign, the rest of the footage would probably be darker than most would like, even if the brighter option are most often also not useful.
Take this video of mine, even if my speed are quite modest and the plates on the parked car are ultra readable EU plates, well it is still way too fast for the conditions.
This old video in the start at the roundabout the car i turn in behind you can actually read the plate AU 33 579
Later at 3:00 on the slow street with parked cars, well i almost capture the plate of the parked white car at 0.25 playback speed, but it is not there on the youtube video at least.