This is something that comes up often, usually among Benelli fans, of which I am one, but many Benelli fans fail to educate themselves on the minutia of shotgun action types and instead use a term that was trademarked by Benelli to describe an action type. And, I honestly should not have risen to this. It is akin to chastising folks for calling magazines clips.
What operates the gun again? Inertia? For inertia to exist, there first has to be some sort of motion caused or already extant. That initial motion, in this instance, is caused by the firing of the shotgun and the resulting recoil of that fired shot. If there were no recoil, the gun wouldn't function just like any other recoil operated gun.
"Inertia" is just what Benelli calls this recoil operated system. They patented a floating bolt mechanism and called it Inertia Driven. It is not an inertia action or inertia operated. It is operated off of recoil which then sends the bolt rearward and back forward through a system of springs.
The Browning A5, Rem 11, and Franchi AL48 are all "long" recoil operated. The barrel follows the bolt back. The Benelli is a fixed breech design and the bolt cycle is "delayed" by the isolator springs for a moment until the "Inertia" spring throws the bolt back. This is not known as short recoil operation in the traditional sense since the barrel needs to move for that system as well but the action is still driven by recoil. As I mentioned earlier, it is more like a fixed barrel/breech delayed blowback. The delay is caused by a spring action bolt.