My dad was using a powder-actuated concrete nail gun for some remodeling not long ago. It used .22 loads to drive nails. The sound it made was eerily identical to the real thing.
The system will have to distinguish real firearms from other powder-actuated hardware. Otherwise it's going to become useless anywhere near a construction site.
I think the best way to distinguish between firearms and nail guns would be with a man in the loop listening to the sounds (which they appear to have). Construction doesn't sound like a firefight.
But what if you shoot a person with a nail gun?