- Must want to be part of the group;
- Must be able to (and want to) communicate with the group;
- Must want to relate positively to the community, in some way;
- Must be able to (and want to) visit or even live in communities;
- Must be able to perform most basic actions.
As I went on to explain, there are a couple acceptable ways to deviate from the criteria. First: players who want a little bit of a challenge can violate the first four criteria in a superficial way (the ogre who wants to be human and civilized, the beast-man who disguises himself so he can live in a town.) The trick here is that a player must abide by the criteria even if, in the context of the fiction, it looks like the character doesn't fit. You can be the loner character who says he hates people and doesn't need anyone, but who feels compelled to help out, anyways. You're pretending to be a loner, but really you aren't a loner at all. This may be because the player has high aesthetic intentions about exploring what would transform a loner into a true companion, or it may be just because the player thinks "grouch with a heart of gold" would be a fun thing to play.
There's also special consideration for a campaign that violates one of these assumptions. If there is no group to be a part of (GM is running a game for only one player, or the game is arranged as some kind of PvP conflict right from the start,) then #1 and #2 aren't as important. Similarly, running a game about rebelling against authority might make #3 or even #4 less important.
The point of the criteria is not to forbid campaigns deliberately designed to violate those principles, but to act as red flags when one player goes against the group's intentions for those criteria. Someone deliberately going against what was planned is probably a special snowflake, in the sense of someone who's aim in playing is to switch the focus to themselves.