Not wearing seat belt? Big no no. Aren't some airbags designed not to go off when seat belt is not on - and it wasn't the sensor wire was cut?
The airbag deploy very quickly, it's hard to believe that they didn't deploy because wire was cut - the signal to deploy would travel a lot quicker than the damage to wiring.
I think the passenger side won't deploy if no one is in the seat. Looks like that was more of a side impact and maybe not "hard" enough to set it off. I also agree with you that the bags would go before the wire is cut