Yknow, I know we like making fun of Kaiba for being so obsessed with Atem that he builds a portal to the afterlife "just to challenge the pharaoh to a card game", but I find it so fascinating at the same time because in many ways, Kaiba's grief feels a bit like a reflection of the fans' grief about Atem's departure.
Granted none of us can do the insane bullshit that Kaiba can lol, but many fans do think that having Atem depart isn't real closure, no? For many, Atem dying in this way isn't him 'moving on', it's him just, dying. He was a boy who never got to be a man, a boy who never got to live, and according to the narrative the only way he gets to live is to... die? The hell does that mean, bish he should've stayed! He should've gotten to experience life's ups and downs, play card games, eat falafel, just live life. This is absolutely unfair, it doesn't fit with the story's theme of choice vs. fate, and so and so forth.
And so going to Kaiba, I think a bit of his grief represents that. His lack of closure in his relationship with Atem, the one person who managed to understand him, whose strength he respected, hoped to surpass... is just fucken dead? The hell does that mean, bish he should've stayed! I needed to beat him! I needed him to be here! I need my fucken friend rival back!
And because of that, he goes through everything possible to bring him back. He takes the Puzzle, he disregards Yuugi's worth as just "a vessel", and even after, he still builds that damn elevator just to see Atem again. It's that wish of "he needs to come back" that fans have, only to its absolute extreme, and I find that parallels to it very interesting.