"Is part of Kaiba's soul in this doll?! His undying grudge...His thirst for vengeance?! Kaiba...! Will you always be my arch-rival!?"
We pick up exactly where we left off: the middle of Joey/Jonouchi's duel against Mai. It goes essentially exactly the same as in the anime with Joey/Jonouchi getting psyched out initially by Mai's little trick of spraying her cards with different perfumes so she doesn't have to look at them before she plays them, but after figuring that out things go very badly for Mai very quickly (thanks in no small part to 'Yami' Yugi's backseat dueling) and Joey/Jonouchi wins the duel--much to Mai's consternation. And thus begins the 'will they, won't they' Joey/Mai background storyline as after the duel he gives her a cheeky wink and a riddle about something more valuable than winning: 'something you can show but you can't see.'
Immediately following the end of this duel, the gang run into (and try to steal fish from) Mako/Kajiki and so commences a duel only made memorable because it's the context for the 'I'm going to attack the moon!' meme -- arguably the first duel that jumps the shark in terms of sheer out of pocket insanity. I actually liked this duel better in the manga than the anime -- something about the aesthetic of this 'duel' (can you really even call it a duel???) worked better and felt more fluid on the page than the screen. I think when it was adapted for the anime they tried to make it feel more like a duel than like a D&D mission which just highlighted how incomprehensible it was as a duel and made it boring.
Next, we get a few chapters of moving the actual plot forward. The manga does a much better job than the anime of keeping the actual plot coherent (it's still insane, but at least the insanity is built up so that all of the other main events feel like part of a bigger background narrative).
Because Yugi is the protagonist, the anime writers tried to force the plot to revolve around him while at the same time still keeping in the Kaiba Corporation takeover storyline and by halfway through, I couldn't tell you why the Duelist Kingdom tournament was happening. In the manga, however, it's really clear that Yugi is (initially) only involved in any of the action because he defeated Kaiba in an official match at the end of the Death-T arc. Duelist Kingdom is actually a game of tug-of-war over Kaiba Corporation between Kaiba and Pegasus that Yugi is stuck in the middle of.
So then having Mokuba show up feels less out of left field because he's able to give a coherent explanation for why Pegasus knew or cared about Yugi in the first place. And it also is made clear why Pegasus had him kidnapped (I’m not saying it's a good reason, but at least it's a reason).
Another thing the manga does that makes more sense (while still being crazy and weird) is the 'Yami' Yugi vs. not-Kaiba duel. Instead of the convoluted 'I'm the ghost of Kaiba -- oh wait, actually I'm the darkness that was banished from Kaiba's heart - - oh wait, I'm a clown dressed up as the ghost of Kaiba (???)'...thing, it's just a creepy ventriloquist using a puppet that looks like Kaiba. And again, because Takahashi kept it straight that at this point in the story Pegasus has much more of an established relationship with Kaiba than he does with Yugi, the point of this grotesque and bizarre interlude is not really to screw with Yugi by making him think Kaiba died (???), but to make a mockery of Kaiba in front of his brother, just to be cruel. It makes Pegasus feel more villainous, and it's also an on-brand manifestation of his particular style of 'cruelty, but make it camp.'
Anyway, so Yugi duels the Kaiba puppet which, from afar, snaps Kaiba out of his post-Death-T coma, and this causes the stolen Blue Eyes White Dragon in the puppet's deck to vanish, allowing Yugi to win the duel. This was the one thing I prefer in the anime. In the manga, I don't really understand why this happened, and it doesn't really tell us anything new about Kaiba as a character, whereas in the anime Kaiba actively causes this to happen (we also get the Kaiba mansion bunker, and we get to see him karate-chop and hurl one of Pegasus's goons) and we get to see the connection between Kaiba and the Blue Eyes White Dragon and also the first instance of Kaiba working on Yugi's side, which is a nicer bit of character growth than him just...waking up.
The rest of the volume is the build-up to and then beginning of the Joey/Jonouchi vs. Rex/Ryuzaki duel, so nothing else really happens plot-wise, and it's a bit of a strange note to end on considering the comparatively higher stakes of everything that came after Yugi defeated Mako/Kajiki.
But, the tournament must go on!