When a wizard has draugar activated (leech ability talisman) the leech animation plays when successfully destroying a web.
I'm guessing that the presence of the friendly creature, which you are freeing, inside the web is what triggers it.
Not sure if this applies to vamps as well.
Leech animation plays when attacking/destroying web
Re: Leech animation plays when attacking/destroying web
In addition to this I've noticed the leech animation always plays when you hit something in law mode. Obviously attacks cannot fail in law mode so the animation is playing as if every hit is a killing blow (when of course it isn't).