Understaffing is absolutely a factor. Had tower and ground not been combined, the erroneous clearance probably wouldn't have been issued.
The ARFF truck not complying with the stop instruction is absolutely a factor. Had they heard and complied, the accident wouldn't have happened.
And there are likely additional factors that will come out in the investigation.
I recommend reading some final aviation accident reports from the NTSB to learn more about how these investigations proceed and what kinds of conclusions and recommendations they include.
Watch the video.
Other trucks slow down, but truck 1 does not even try to slow down. I'd also argue that driving so quickly that you cannot maintain control is its own problem. Getting to an emergency 20 seconds later almost never matters as much as arriving safely.