So schadenfreude would fall under envy — even if one did not envy the person in whose downfall one gloried? (e.g. Tony George; Michael Schumacher).
In that scheme envy is insufficient love of our neighbor's good, and certainly "rejoicing at the evil"(1 Cor 13 somewhere or other) is a severe case of failing to love my neighbor's good.
So Spitzer's downfall is a spiritual temptation, and we have, I think, to suppress the urge to cheer and instead to thank God that we have not been so tempted and not so succumbed and to pray that this calamity (for him) be an occasion of his turning to God in repentance.
Yeah, I know that sounds pious, but that's my current struggle as regards Bro. Spitzer.