And then you exclaim: "Haha, du Schaf!"

Not really. The best example of Schadenfreude (imo) is when you follow a sports team (probably not too many of you here on Lemmy), whenever the rival team loses you feel Schadenfreude. There doesn't have to be any kind of 'just-ness' to it, actually if the rival team losses unjustly (played better, but were unlucky) the Schadenfreude is actually greater.

Of course there are times when something bad finally happens to someone that deserves it and you feel joy from it, but I wouldn't call that Schadenfreude, more like 'Vergeltungsfreude'.

While 'Schadenfreude' literally translates to the joy of damage, 'Vergeltungsfreude' would translate to the joy of retribution. Source: my German ass

Is there a fun German (or any other language) word for taking delight in the pain of others when it totally is their fault, and their fault alone?