Crash probably a couple seconds later, wouldn't rely on the video for the exact timing.
So it seems that ATC made an error by allowing the truck to cross, and then the order to stop wasn't communicated clearly enough. I wouldn't place much blame on the truck.
Edit: Looking at some other videos with that audio, I'm also not sure if the video I linked represents the time between communications correctly, transmission at 3:15 may have been right after the one at 3:02. Anyway, the best thing is to wait for the investigation.
Truck declared it was crossing. ATC told it to stop. Truck didn't stop.
This wasn't a communication issue.