According to Japanese bloggers who went to the screening, Pegasus is killed near the beginning of the movie. Murdered by Paradox, with him screaming "OH NO!"...I'm assuming this is young Pegasus, before he even gets the Millennium Eye or creates Duel Monsters.
But the losses don't stop there. Paradox apparently kills Yugi's grandpa too. This is apparently the really bad event that the creators said would happen to Yugi, over the course of this.
So Yusei looses his ace card, while Yugi loses his grandfather. I'm not sure what Judai loses, but its apparent that Paradox is systematically taking something from each main character, or at the very least, fucking their shit up, really bad.
That being said, it appears a Grandfather Paradox is created thanks to Paradox's actions, and that's the setting for this duel. And Paradox is apparently tearing up everything with his Sin monsters.