Your GPS says 29 MPH, presumably the other car was going a similar speed since it looks like a 30 MPH speed limit, so a closing speed of 29 x 2 = 58 MPH = 26 meters/second. 26 m/s / 120 fps = 217 mm/frame.
So if the exposure time actually took the full frame interval then there would be 217 mm of blur on his number plate and it is not surprising that it is unreadable. It appears to be rather less than that so the exposure was rather faster than 1/120th second.
Exposure time, and thus motion blur, has almost nothing to do with frame rate.
120 fps is great for making slow motion movies, but otherwise is probably not much use, especially as my computer struggles to play it smoothly!