I found an interesting two-person kata that Asgarda performed 5 years ago - it's more performance art or dance tinged with martial arts, but it IS unique:
I've heard and seen differing interpretations of Asgarda, ranging from a martial club for girls to a quasi-religious cult; I've heard that they adore men or that they despise them, and that they want to support them or totally separate themselves from them.
Katerina Tarnouska has been quoted as saying that the "Time has come to get separated from the men". She "dreams of a walled world where women would live among themselves".
That's a far cry from what she was trying to portray in your video.
As to the martial aspect - it's kickboxing, that's what she knows. It's a nice basic art for self-defense as long as she leaves out the point-fighting aspects. The weapons? Probably used to mix the training up, keep it interesting, because like so many other martial arts weaponry it isn't modern enough to think you'll be carrying it down the street with you when you need it. The
kama (sickles) that they're using, for example - farming tools, and a traditional Japanese weapon.