Here's something I don't think people have paid much attention to:
A conquest or domination victory requires having developed and deployed a powerful military and having crushed your oppoents. You are the most powerful military player in the game - and may well lead in other respects, such as cities, population, and perhaps even science - when you win.
A Time victory represents having the highest total score, and thus the "best" civiliztion at the end of the game. You might split hairs over the specific formula used for calculating score, but no civ that's not genuinely a leader in the game can win this way - it still requires being the best, even if you're just edging out second by a small amount.
Cultural Victory reflects having the most powerful culture - generally awesomely more powerful than your opponents. (In order to achieve this you're probably also doing OK in terms of technology and perhaps militarily in order to defend it, but not necessarily.) It represents being the best in one area requiring massive investment, and possibly other areas. (I also think this victory is pretty tough to achieve.)
Space Race Victory generally requires at least technological parity, if not leadership, and significant production capacity, along with good timing. You may also need a non-trivial amount of military to defend your construction. There's certainly no way to pull off a surprise space race, and it represents a huge amount of work.
UN Diplomatic Victory requires having the support of the majority of the world. You not only had to build the wonder, you had to build the relationships. You're civilization is large, successful, and well liked enough to be supported by more than half the planet. (Is it 2/3rds? I forget.)
So what does the Apostolic Palace Victory require/represent? It seems to be the only victory condition by which the weakest Civ can "come from behind." In a game with few players remaining, it's actually better to NOT spread your religion much. You don't need the largest population, highest score, any particular military strength, production capacity, or technology. It represents nothing more substantive than building a single wonder and having barely spread your religion.
That's my problem with it. Well, my main problem - in so much as the game is a "simulation," I just can't get past my problem with the idea that the less populous civ suddenly wins because a few guys in ONE of my border towns happen to follow another religious leader. 99% of my people are NOT their religion. I have more people, money, military might, production capacity, etc. yet they suddenly win? In what way are they better? How did they achieve more? What world is this? What situation does it represent? How is this "realistic" (yes, I know not everyone has "realism" issues with elements of the game) is this?)
If I were naming it, I'd call it "the terrorist victory." The sleeper cell in your border town creates enough fear and panic that the mightier civ just caves in to the demands of the foreign religious leader. (That doesn't seem very realistic, either.)