Is it Schadenfreude to take pleasure in the death of an enemy? Only if it is bad to be dead. But it is not clear that it is bad to be dead. On the other hand, if it is bad to be dead, it might still not be Schadenfreude to take pleasure in the death of an enemy.
For I might take satisfaction, not in the fact that my enemy is dead, but that he can no longer cause me trouble.
But you want to know what Schadenfreude is. This is from an earlier post:
If to feel envy is to feel bad when another does well, what should we call the emotion of feeling good when another suffers misfortune? There is no word in English for this as far as I know, but in German it is called Schadenfreude. This word is used in English from time to time, and it is one every educated person should know. It means joy (Freude) at another's injuries (Schaden).
The great Schopenhauer, somewhere in Aphorismen zur Lebensweisheit, remarks that while envy (Neid) is human, Schadenfreude is diabolical. Exactly right. There is something fiendish in feeling positive glee at another’s misery. This is not to imply that envy is not also a hateful emotion to be avoided as far as possible. Invidia, after all, is one of the seven deadly sins. From the Latin invidia comes ‘invidious comparison’ which just means an envious comparison.