I've never seen Aiki in Aikido weapon work, so I don't know what to call it other than aikido weapons.
Since it seems to match aikido movement of ___________________flavor of any group, there's really nothing to discuss ...its just a bunch of people having fun....until the mid dan and kyu ranked people start to once again " imagine" they're doing real weapons, or that what they're doing is aiki.
First time I saw Aiki was in a game my father showed me. Then I saw it in handball and in football. I found it in nature. And in working with animals. I found it in western boxing, fencing and in kempo. I saw it in Aiki weapons. But it took a long time before I saw anyone do Aiki in Aikido !
All the best!