Hahahaha, I was just talking in the chat about the meaning of Sin
World. Then I saw your post. Hivemind, man, hivemind! :V Anyway, my take
on Sin World:
It appears to be a space field which transforms the entire area. Space
is supposed to be vast and infinite, and in a sense, empty. It could
represent the state of Paradox's future - the world is still vast, but
nothing remains, he is alone. The Sin of mankind (their acts, or through
Duel Monsters) have wiped everything out. The vast space is Paradox's
loneliness, showing that this is the infinite end, the future is ruined.
The way the Field Spell transforms the city has other meaning as well.
We know that at this point, the reality is slowly falling apart from
Paradox's changes. Paradox's goal is to destroy Duel Monsters, to
eliminate the past to save the future (presumably destroying it, thus
preventing the destruction from ever happening). The space field gives
the place a semi-non existent appearance, as if it is still there, but
it is about to be replaced by nothingness. As if the entire reality was
warped into that state, the impending erasure, nothingness and
loneliness...
Why is it called Sin World? You could see the ruined future being the
result of Duel Monsters/mankind's Sins, so in a sense, it is a world
produced from that Sin.