Update: Scratch that, it makes a very confusing introduction o.o, I have been starting to make updates my analysis posts about the Duelist Kingdom Arc to restructure it into the same structure as Battle City Arc and Memory World Arc.
Plot Summary:
They arrived the Duelist Kingdom island, they walk a little and participants and the gang in front of a castle gate and at the castle's balcony to welcome them and explain the rules of the tournament in a very "battle royale" fashion around the island and the time limit of the tournament is two days (48 hours) and the contestants who have less than 10 stars can't go to the finals.
After the rules been explained, the gang explores a little of the island for Dark Yugi follow Haga's trail and Haga challenges Dark Yugi to a duel, he accepts by betting his only one star and his life as Haga betting his two stars, the duel at first takes initial lead on Haga, but the moment he turn the tables, the back and forth starts between Haga and Dark Yugi, it's not only the gang watching being the first duel, the other contestants are watching too and among them is Mai Kujaku as a commentator for the gang being a more experienced duelist...the duel ends with Dark Yugi's victory and Haga having lost both his two stars is the first to leave the island.
Key Points:

Dark Yugi worried about Jounouchi in possibly getting a cold and apologising, so sweet and is not often we see him doing so, even Jounouchi was kinda moved because he responded with "Aww, this is nothing!" and he is right about what ticks him off in throwing Yugi's cards (more technically Yugi's granpa, specially being Exodia, I would feel so bad and irritated, because it was of someone close 😖).
Regarding what Dark said to him and now thinking that he will taking him down first, he means in literal sense, he is determined in putting Haga out of the tournament first.
Then Pegasus starts announcing the rules of the tournament, he mentions they have to use official licensed cards of the game, I find it interesting and then advices the other duelists if they aren't satisfied with their decks, they trade with one and another...

It was a very high risk to begin with just from Dark Yugi giving away one of his star chips, which implied that they would have to use it in some way, with these conditions explained, Dark Yugi and Jounouchi have to win their very first battles, but then when we think Dark Yugi giving one star to Jounouchi of his own accord to give him a fighting chance, it's only logical and fair having these kind of conditions.

After Pegasus, explains the rules, and mentions the battlefield it's around the island, "battle royale" style, being around the island, Dark Yugi starts questioning by what meant by that, from a participant's perspective since a card game tournament just need a room filled with tables and not around a huge area such an island for a TCG Tournament and quickly comes to the conclusion is related to the new rules, this proves his quick thinking, I wouldn't call just quick thinking that he does.
On the subject about the rules, Pegasus says there is a time limit to be 48 hours, in other words two days and to enter the castle, the participant must have 10 stars and moving to the semi-finals.
But one can keep wondering with this many contestants, is it two days even enough? I don't think it is, from how treated his contestants of not even providing a sleeping bag and force Yugi into this tournament, something fishy going on, the tournament won't be that smoothly as Pegasus make it sound and is more to say about how much of a awful tournament host he is...
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