With all the controversy around animation canceling recently

I don't think there's ever been any controversy around animation cancelling, like, ever. Also, basically everybody already knows about and actively uses the CC "cancelling" you've done in your video.

That is animation cancelling? Pretty sure that's just how spell priority between clashing spells is handled in the game.

If 2 spells are cast and they clash against each other, CC in particular are the most noticeable, the one that's cast later get higher priority of execution. This is why for instance, Ezreal can blink after he's already caught by for example Blitzcrank's hook and walk away like nothing happened, or if you're Ryze and you W someone and they dash at the same time but slightly later then they will only be rooted after the dash is completed. This is the same here. Urgot cast his E after Vayne's E and so he broke her knockback; though I am not too sure what happened at Alistar's case there, but seeing them BOTH got CC'ed and then interrupted by each other, it's probably due to how Alistar's W is coded as it may have been coded differently than other conventional spells to make it happen.

I'm not saying I'm for or against whatever is shown in the clip or whether or not I support animation cancelling, at least here in this thread anyway, but I don't think that's animation cancelling.