Not sure if it was different in the manga, but in the anime, Yugi (Well okay, Atem) dueled Pegasus through a magic TV, lost, and so he took Grandpa's soul, and told Yugi the only way he was getting it back was to enter the Duelist Kingdom Tournament and try and make it the finals to duel Pegasus one last time, but if he lost that duel, Pegasus would get his Millenium Puzzle. The whole reason he challenged Yugi in the first place.
So why didn't he just take it the first time?
Instead of just taking his Grandpa's soul, why didn't Pegasus just take Yugi's Millennium Puzzle? Penalty games seem to not have any limits to what a person can "wager," and I heard in the manga the things a person could lose range from the sanity to even their luck, so why wouldn't Pegasus use his ancient Egyptian magic to take Yugi's puzzle after he beat him? Was his motivation different in the manga? In the japanese version of the anime?