Its at the end of the clip, watch carefully, Katarina goes airborne from azir R and then blinks from mid air.
AP Ez was always my jam back in the day so naturally I have to make it work. I am shocked to see people not bringing up shiv, it gives 45 AP now and helps so much with clear. I skip muramana all together because its on hit effect doesnt work with shiv (for some reason) and I go gunblade second. The AD from shiv + blade plus shocks gives you a surprising amount of clear.
After you gotta go into lich then rabadons and at 4 items you can pop people hard, but even earlier with just shiv + gunblade components you still pump out damage.