In the video and in game he uses and swings it as if its a sword but it appears as some kind of blunt energy bat or something similar too.
Also is his weapon tied to the device on his back at all besides just looking similar?
It is actually one of the clock hand's on one of the larger Piltovan Clock Towers. It is not a sword or a cricket bat or any of that mumbo-jumbo.
It's a four-dimensional cricket bat.
As for whether or not it is connected to the hourglass on his back, I suspect it is. After he hits people enough they slow down, and he speeds up. Sounds like time shenanigans to me.
Its a lightsaberbat
Who cares?
There are plenty of champs who appear to have little to no use for the weapon they have in hand, yet no one questions it. 
