In TRANSCEND GAME, the prequel manga, Kaiba knows about Atem's name and that he died which may seem strange at first since in the manga continuity, he wasn't there for the Ceremonial Battle. However, at the end of the manga, Kaiba and Mokuba were outside the shrine of the Millennium Stone when the group left, making it possible for him to have learned about Atem leaving for the afterlife from them.
Kaiba's motivations and obsession with dueling Atem makes more sense when you look at the end of the Memory World arc. At the end of the RPG, Priest Seto thinks he can't become king until he defeats Atem, who passes on before they can fight. In the modern day, Kaiba has always wanted to be King of Games and plans to become king of the Duel Links system, but has always been beaten by Yami Yugi/Atem. And once again, the guy passes on before Kaiba could win the title from him.
We don't know what happened the first time though, as we only have the event of the RPG Shadow Game. Since Atem sacrificed himself, Seto may have only found out the Puzzle after he did it so he couldn't have not say goodbye to his cousin. Likewise, Kaiba wasn't there when Atem died and therefore couldn't say goodbye.
Alternatively, the real reason why Kaiba is so obsessed with Atem is in part driven by a key aspect of his character (at least in the Anime Dub): His tendency to try to destroy his past, or at least to stomp it down rather than truly face it. Every arc he's had generally had him be utterly dismissive towards the intended message being sent to him; that he can't avoid his past and his past mistakes forever, and that sooner or later they'd come back to haunt him unless he faces his inner demons. In each case however, he's always been able to brute force his way through, with the only exceptions being when Mokuba was threatened. As such, he's never had to internalize the intended message, and basically went on his merry way while his past opponents or tormentors basically had to deal with it. But then there's Atem. He has decisively proven to be Kaiba's superior in dueling, and Kaiba has never been able to break him down the same way he did for everyone else. Because Atem is the one that got away, a loose end that Kaiba cannot ever hope to deal with. For a Control Freak like Kaiba, who's built his entire ideology on breaking down the things that negatively affect him until they stop being a problem, this would drive him utterly up the wall.
In his first duel with Aigami, Kaiba summons Obelisk the Tormentor through sheer willpower. This makes sense when you remember that he's the reincarnation of a man who inherited the role of Pharaoh, so the Egyptian Gods would be willing to protect him if he called for their help in a Shadow Game.
Better yet, the room they duel in is very close to the Millennium Items and the physical copies of the God Cards, probably directly above the area they'd have been lost in. It would not be hard for Kaiba to essentially channel Obelisk for this duel.
After it is revealed that the opening duel with Atem was just a simulation, Kaiba angrily declares that it wasn't like dueling the real Atem. And he does have a point. The turn prior to his defeat, Simulation!Atem used Magical Dimension, a quick play spell card to summon Dark Magician Girl and destroy Kaiser Vorse Raider. Kaiba was then left wide open for a direct attack, which he blocked by using a face down card to end the effect which had his Blue Eyes banished. Had Simulation!Atem instead simply attacked Kaiser Vorse Raider and then used Magical Dimension to take out Blue Eyes when Kaiba tried to summon it, he likely would have won.
It goes a bit further than that even. During the duel, Kaiba thinks to himself about how Atem was always able to come up with strategies that his opponent could not predict and for a good chunk of the duel, the Simulation!Atem was indeed coming up with strategies that kept Kaiba on his toes... until the final card. Not only did Kaiba predict the Simulation!Atem's final trap card, but had the perfect counter to it waiting that won him the duel almost instantly. If the simulated Atem had lived up to Kaiba's expectations of unpredictable strategies, he would not have been able to do so.
The manga cryptically◊ implied◊ that Yami Bakura has some history with Shadi. This gets elaborated on in DSOD.
Yugi gave Kaiba "Monster Reborn" as part of the cost to activate "Magical Contact Door". While this may seem to be a small detail, it's symbolizing that Yugi accepted Atem going to the afterlife, while Kaiba doesn't.
While the movie itself doesn't explain some of the cards and moves made very well, looking at the real life cards shows that the majority of the cards showcased in the movie were played correctly. In fact, you can tell exactly what happened in the final move of the movie when you glance at the text of Palladium Oracle Mahad.
The rules of Dimension Summoning are similar to the ka battles and the damage that Zorc caused during the Memory World arc. The imagery of the Plana when used for evil, and the description of the world that would be left if the Plana was used by a person filled with hate, both highly resemble the Shadow Realm. Considering the evil spirit of the Millennium Ring (which used to contain a part of Zorc) is what ultimately tries to remake the world into that dark place, and Zorc was the one to originally create the Shadow Realm, it really ties the various parts of the plot together when you think about it (though only in the dub where the Shadow Realm was a thing).
The "Shadow Realm" thing, however, is entirely made-up for the Dub. Zorc was born from the collective darkness in humans' hearts in the original comic and Japanese version of the show. The reason for the "Kiai to Summon at Max Power!" shtick was more in-line with the original "magical quantum physics" metaphysics of the movie, in that the Prana manipulated reality by their personal & collective willpower. The Zorc / Prana connection simply doesn't exist in the original version, and any similarities in the dub are entirely coincidental.
In the Japanese version, the magical metaphysics are... slightly hard to grasp at first. Basically, Aigami and the other Prana work because of magic Quantum Mechanics, and the idea of a Collective Consciousness; the sole reason anything, or any ONE, can exist is because they're being observed by another. The reason Aigami's victims are disintegrated is because he throws them into a subdimension made up of only their own memories; because a person cannot observe themself, they begin to disintegrate on a quantum level until there's nothing left. So how did Jonouchi survive, when everyone else was literally entropy'd to death? In a bit of foreshadowing, what Jonouchi thought was just a memory of Atem actually was Atem. Since Atem has passed on, he is able to cross dimensions, like the Prana Children, and helped out Jonouchi the same way he helped out Yugi later (in Egyptian mythology, the deceased often aided the living in small but impactful ways, so this is a nod to that idea). Because Atem appeared in the subdimension and actually observed Jonouchi, Jonouchi fell back into Quantum Certainty, thus returning himself to the real world. All this was glossed over in the dub because it's a fairly strange idea that 4K probably felt would have gone way over the heads of its intended very-young audience. (Remember that the Shounen demographic of Jump in Japan tends to err closer to the 12-16 range than the 8-10 range of the Dub in the US)
Shadi's retconning of the Millennium Items as representing a Balance Between Good and Evil actually makes perfect sense in context; The Ring, Eye and Rod are prone to evil because they were the items directly exposed to Zork's power 5000 years ago, with the Ring as Zork's Soul Jar, and the wielders of the Rod (Seto) and Eye (Akhenaden) both being possessed by Zork at one point. Meanwhile, the Necklace, Key and Scales were not exposed to Zork's power, and the Puzzle containing 'both Light and Shadow' refers to it being the container for both Zork's Darkness and Atem's Light.
From all the source material so far, Kaiba doesn't seem to be wearing his locket. That might mean he and Mokuba aren't as close, which could partially explain why he's more antagonistic in this, and more willing to leave Mokuba behind. The only question is why they aren't so close anymore.
According to Aigami, thanks to Kaiba nobody in Domino City can have citizenship without a Duel Disk. Transcend Game says his latest dueling system collects data from the brains of the Duelists themselves, and he can track anyone in the city by their disks or brainwaves. Suddenly jokes about Kaiba being a dictator aren't as funny, and Joey's subplot about needing a new Duel Disk makes more sense when he could be banished for not having one.
Whether he comes back or not, Kaiba left Mokuba, a thirteen-year-old, in charge of his company. Given what happened the last time Mokuba had to protect it it's probable KaibaCorp's enemies may capitalize on the situation.
Kaiba talks about how the world they live in is so poorly-constructed that he'd fire whoever was responsible, with some translations going as far as to have him say he'd kill whoever was responsible. In the official translation of Transcend Game he also talks about going to the afterlife to put an end to Atem, which could be interpreted as killing him as easily as dueling and defeating him.
Mother's Basement has a video on the popularity of the card game In-Universe and came to the conclusion that Yugi's dream of being a game designer is doomed to failure with the massive monopoly of influence and economy Duel Monsters has over the world.
◊ implied
