Just a variation of the figure-8.

Another short video

Sequence

I'm not confident enough with the names of the styles to really know but I thought that Byzantine was a over head style with a side arm finish same singe rotation realease.

If so I feel like this styles somewhere between a Byzantine and a Figure 8. Thought it was a weird one but getting pretty decent power and accuracy only a few days in.

I've had a play with an empty sling and I'd say it depends how you look at it as it has similarities to both.

The direction of the initial swing is in a different direction to a byzantine throw. Instead of swinging outwards and round to your front (as in a sort of sidearm throwing motion), the initial swing is upwards and behind you (like throwing a backpack over your shoulders).

If you throw fig-8 there are effectively 3 'swings'- each feeding into the next. First is the drop and swing backwards under you, second is when it swings back round behind you and third is the overarm launch.

What you are doing here is shortcutting the first stage of fig 8 and going straight to the second swing- where it rotates behind you into launching position. For this reason the throw is essentially fig 8 only without the first swing.

Another way you could look at it is the throw is like a byzantine in action but with a different direction. Both have a two stage rotation which feels similar and start from a hanging position. The traditional rotates upwards and sideways whilst your version rotates round behind then forwards.

I would probably call it a 'short fig-8' or 'hanging fig 8 variation' OR you could call it something like 'inversed byzantine' or 'reverse byzantine'.

I might even lean towards the latter since the throw arguably doesn't really draw a fig 8 anymore, even if the throwing direction is much closer to a fig 8 than a standard byzantine.

IT's what's called: Byzantine.

No idea why or who coined the name - but that's what it is

Good simple throw for distance.

And can you PLEASE get a bloody youtube account and resize your pictures before uploading.

Judop I think explained it well. Sometimes a throw has elements from different throws in it. Additionally not all figure 8's start with a drop. For me the crux of the figure 8 is switching from sling side  to the other than back with the switch being somewhat vertical. Although the actual pitch itself could be horizontal. 

Granted I cant see whats going on very well. Maybe you guys are getting a clearer picture of it.  I'm pretty sure it's not a pirouette at least.  Hope that narrows it down.